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The five vowel letters can be arranged in (5!) = 120 ways; and for each arrangement of these vowel letters, the four consonant letters can be arranged in (4!) = 24 ways. Therefore, the answer will be in (120*24) = 2880 ways.
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How many ways the word EDUCATION can be arranged?

Hence, the total number of ways = 4!
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How many ways EDUCATION can be arranged so that no vowels are together?

Hide Show timer Statistics – In how many ways can the letters of word “EDUCATION” be arranged such that NO two vowels appear together? A) 9! B) 5!*4! C) 5!*5! D) 5!*4!*2! E) 6!*4! _ GMATinsight Great Results (Q≥50 and V≥40) l Honest and Effective Admission Support l 100% Satisfaction !!! One-on-One GMAT Skype classes l On-demand Quant Courses and Pricing l Admissions Consulting Call/mail: +91-9999687183 l [email protected] (for FREE Demo class/consultation) SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l GMAT730+ESCP FREE Resources: 22 FULL LENGTH TESTS l OG QUANT 50 Qn+VIDEO Sol. Joined: 20 Mar 2014 Posts: 2415 Concentration: Finance, Strategy GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) Re: In how many ways can the letters of word “EDUCATION” be arranged such 08 Jul 2015, 06:50 GMATinsight wrote: In how many ways can the letters of word “EDUCATION” be arranged such that NO two vowels appear together? A) 9! B) 5!*4! C) 5!*5! D) 5!*4!*2! E) 6!*4! No 2 vowels together = the only arrangement possible will be V C V C V C V C V (with V=vowel, C=consonant). This is true as we have 5 vowels and 4 consonants and any other combination will force us to pair 2 vowels together. Thus, the number of arrangements possible : 5 *4 *4 *3 *3 *2 *2*1 = 5!*4! -> B is the correct answer. _ Senior Manager Joined: 15 Sep 2011 Posts: 279 Location: United States WE: Corporate Finance (Manufacturing) In how many ways can the letters of word “EDUCATION” be arranged such 08 Jul 2015, 10:30 There are five vowels and four consontants. The consontants must be placed in between each vowel in order to fulfill the requirement that no two vowels touch each other. Thus, answer choice B. \(5! * 4!\). Answer choice A, C, D, and E don’t make sense.

A is for when all choices are distinct, but in fact half of them are, vowels or consonants. Answer choices C and E include another integer 5 and 6, respectively, for no reason at all, thereby making the number of selections 10 instead of nine. As well, answer choice D appears as though the selections had to be doubled to count for whether consontants or vowels start first, but the factorial itself accounts for it and none of the consonants could begin first because of the constraint.

So nothing of such is warranted. Thanks, Intern Joined: 05 Nov 2014 Posts: 38 Concentration: Marketing, International Business Re: In how many ways can the letters of word “EDUCATION” be arranged such 26 Jul 2015, 22:52 Engr2012 wrote: GMATinsight wrote: In how many ways can the letters of word “EDUCATION” be arranged such that NO two vowels appear together? A) 9! B) 5!*4! C) 5!*5! D) 5!*4!*2! E) 6!*4! No 2 vowels together = the only arrangement possible will be V C V C V C V C V (with V=vowel, C=consonant). This is true as we have 5 vowels and 4 consonants and any other combination will force us to pair 2 vowels together. Thus, the number of arrangements possible : 5 *4 *4 *3 *3 *2 *2*1 = 5!*4! -> B is the correct answer. We can consider the consonants as one group: the set looks like, E, U, A, I, O where the is regarded as one item. Number of ways we can arrange the set = 6! (since there are 6 items) Number of ways we can arrange = 4! Required arrangement = 6! * 4! OA is E GMAT Club Legend Joined: 08 Jul 2010 Status: GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator Posts: 5915 Location: India GMAT: QUANT EXPERT WE: Education (Education) In how many ways can the letters of word “EDUCATION” be arranged such 26 Jul 2015, 23:24 Subanta wrote: Engr2012 wrote: GMATinsight wrote: In how many ways can the letters of word “EDUCATION” be arranged such that NO two vowels appear together? A) 9! B) 5!*4! C) 5!*5! D) 5!*4!*2! E) 6!*4! No 2 vowels together = the only arrangement possible will be V C V C V C V C V (with V=vowel, C=consonant). This is true as we have 5 vowels and 4 consonants and any other combination will force us to pair 2 vowels together. Thus, the number of arrangements possible : 5 *4 *4 *3 *3 *2 *2*1 = 5!*4! -> B is the correct answer. We can consider the consonants as one group: the set looks like, E, U, A, I, O where the is regarded as one item. Number of ways we can arrange the set = 6! (since there are 6 items) Number of ways we can arrange = 4! Required arrangement = 6! * 4! OA is E Hi Subanta You seem to have read the question wrong. Question says that “such that NO two vowels appear together?” EDUCATION has 5 Vowels A E I O U and all must be separated by atleast one consonant between any two adjacent Vowels and we only have 4 consonants DCTN i.e. in the arrangemtn A – E – I – O – U all teh dashes (-) must be occupied by atleast 1 consonant and since we have 4 places and 4 consonants so every dash (-) must have exactly one consonant.i.e. the arrangement will be A D E C I T O N U where all vowels AEIOU can exchange positions among themselves in 5! ways and similarly all Consonants DCTN can exchange positions among themselves in 4! ways i.e. Total Arrangements = 5!*4! Answer: option B _ GMATinsight Great Results (Q≥50 and V≥40) l Honest and Effective Admission Support l 100% Satisfaction !!! One-on-One GMAT Skype classes l On-demand Quant Courses and Pricing l Admissions Consulting Call/mail: +91-9999687183 l [email protected] (for FREE Demo class/consultation) SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l GMAT730+ESCP FREE Resources: 22 FULL LENGTH TESTS l OG QUANT 50 Qn+VIDEO Sol. l NEW : QUANT REVISION Topicwise Quiz Intern Joined: 05 Nov 2014 Posts: 38 Concentration: Marketing, International Business In how many ways can the letters of word “EDUCATION” be arranged such 27 Jul 2015, 04:37 Quote: Hi Subanta You seem to have read the question wrong. Question says that “such that NO two vowels appear together?” EDUCATION has 5 Vowels A E I O U and all must be separated by atleast one consonant between any two adjacent Vowels and we only have 4 consonants DCTN i.e.

in the arrangemtn A – E – I – O – U all teh dashes (-) must be occupied by atleast 1 consonant and since we have 4 places and 4 consonants so every dash (-) must have exactly one consonant.i.e. the arrangement will be A D E C I T O N U where all vowels AEIOU can exchange positions among themselves in 5! ways and similarly all Consonants DCTN can exchange positions among themselves in 4! ways i.e.

Total Arrangements = 5!*4! Answer: option B Sorry! I misread the question! I need to pay more attention to detail. Nice explanation btw! Non-Human User Joined: 09 Sep 2013 Posts: 25809 Re: In how many ways can the letters of word “EDUCATION” be arranged such 01 Sep 2021, 18:34 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up – doing my job. I think you may find it valuable (esp those replies with Kudos). Re: In how many ways can the letters of word “EDUCATION” be arranged such 01 Sep 2021, 18:34 Moderators: Senior Moderator – Masters Forum 3099 posts
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How many pairs of letters are there in the word EDUCATION?

There are five pairs in the word ‘EDUCATION’, each of which has as many letters between them in the word (both forward and backward direction) as they have between them in the English Alphabet.
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Does EDUCATION have all vowels?

Hint: In order to get this problem solved we need to know the number of vowels present in the word EDUCATION. Vowels are A, E, I, O, U. After that we have to use combinations and select the number of ways. Then we have to apply the formula of probability to get the right answer.

• Complete step by step answer : The word provided to us is EDUCATION.
• We need to find the probability of getting a vowel if a letter is chosen at random.
• We know that there are 5 vowels and 21 consonants.
• The 5 vowels are A, E, I, O, U.
• The total number of words present in the word EDUCATION is 9.
• In which E, U, A, I, O are vowels.

So there are 5 vowels among 9 alphabets. So, the probability will be the number of favorable outcomes upon total number of outcomes. Total number of outcomes will be selecting 1 letter from 9 letters present that is $^9 $. Number of favorable outcomes is the selection of 1 letter from 5 letters that is $^5 $.

Therefore the probability of getting the vowel in the word EDUCATION is $\dfrac }} }} = \dfrac $. Hence, the correct option is D. Note: When you get to solve such problems you need to know that probability is the number of favorable outcomes upon total number of outcomes. You also need to know that there are 5 vowels and 21 consonants out of 26 letters in English.

Those 5 vowels are A, E, I, O, U and any one of those if used in a word than those letters are considered as vowels.
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How many ways can vowels be arranged?

Discussion :: Permutation and Combination – General Questions ( Q.No.2 ) –

2.	In how many different ways can the letters of the word ‘LEADING’ be arranged in such a way that the vowels always come together?
, 360 , 480 , 720 , 5040 , None of these Answer: Option C Explanation: The word ‘LEADING’ has 7 different letters.When the vowels EAI are always together, they can be supposed to form one letter.Then, we have to arrange the letters LNDG (EAI). Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways. The vowels (EAI) can be arranged among themselves in 3! = 6 ways. Video Explanation:

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Shoba said: (Sep 4, 2010) Other than vowels there are only 4 letter then how it s possible to get 5!.

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Sai said: (Sep 10, 2010) HI SHOBA,.4 consonants + set of vowels (i.E., L+N+D+G+ (EAI) ). We should arrange all these 5. So we get 5!. I think you understood.

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Sachin Kumar said: (Sep 29, 2010) Please make me understand this answer as did not get.

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Sri said: (Oct 10, 2010) As vowels are together take (EAI) as single letter i.e., total no of letters are 5 (L, N, D, G, ). No of ways can arrange these 5 letters are 5! ways. Now we arranged 5 letters (L, N, D, G, ). Next we have to arrange E, A, I (they may be EAI/EIA/AEI/AIE/IAE/IEA). All these combinations imply that vowels are together. So we have to multiply 5! and 3!.

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Subbu said: (Jan 6, 2011) 7!=5040

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Madhusudan said: (Mar 14, 2011) Could you kindly let me know what is ( ! ).Howe 5! = 120 ?

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Sundar said: (Mar 14, 2011) @Madhusudan 5! = 5 Factorial = 1 x 2 x 3 x 4 x 5 = 120

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Laxmikanth said: (Mar 26, 2011) When should we take the one or more letters as a single unit and why?

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Moaned said: (Apr 8, 2011) I am not getting

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Jessie said: (Apr 10, 2011) 7 letter word = LEADING CONDITION = VOWELS TO BE TOGETHER, HENCE (EAI) TO FOR A WORD SO NO. OF WORDS = L,(EAI),D,N,G = 5 permuation to arrange 5 letters = nPr= n!/(n-r)!=5!/0!=5! 0! is assumed to be 1!) EAI can be arranged among each other in = nPr = 3!/(3-3)= 3! hence 5! x 3! = 120 x 6 = 720

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Mayur said: (Apr 15, 2011) How it came like nPr formula and how you have solve it? please let me know.

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Bharti said: (Jul 11, 2011) Thanks a lot. I had confusion before your explanations. Thanks a lot.

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[email protected] said: (Aug 5, 2011) @mayur. You just look when ever you open the new exercise there will be availability of basic formulas. If you go through them half of the task would be finished easily. Have a good day buddy.

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Siva said: (Oct 16, 2011) Permutations and combinations always make me to confuse much. How to decide based on the descriptive aptitude question ?

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Shiva said: (Oct 18, 2011) Why we have taken 5 (4 + 1) ?

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Santosh Kumar Pradhan said: (Oct 27, 2011) Total member 7 out of which 5 consonant and 3 vowels take 3 vowls as a 1 hen number of consonant will arrange 5! ways and these 3 vowels will arrange 3! ways though,5!*3!=720

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Bhavik said: (Nov 4, 2011) How to read these nPr ?

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Sagar Choudhary said: (Nov 6, 2011) What is this 5! and 3! ?

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A.Vamsi Krishna said: (Jan 30, 2012) “!” this implies factorial that means a number is multiplied like for example take number 5 then its factorial will be taken as 5*4*3*2*1 and this is equal to 120.

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Ncs said: (Feb 2, 2012) Why not 5! + 3! ?

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Raj said: (May 21, 2012) Friends, How do you say this question is permutation.

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Mahanthesh said: (Jul 30, 2012) Hi guys. As per the question, it s mentioned that all vowels should be together, but it has not been mentioned that it should be EAI. According to me these 3 vowels can be arranged in 3*2=6 ways. And the remaining letters LDNG can be arranged in 4*3*2*1= 24 ways. Can anyone explain me about this please ?

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Sandeep said: (Sep 7, 2012) can any one explain ? y 5!*3! & y not like this 5!+3!

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Srk said: (Oct 9, 2012) @Mahantesh.1. There is given a word LEADING in this LDNG (consonents), EAI (vowels).2. They asked here vowels always come together and so we should have to take LDNG (EAI).3. We can take as (4+1) ! i.e. here we have to take vowels as together as 1. So we have a chance of 5!.4. But with in vowels we have many arrangements i.e 3! 5. Finally 5!*3!

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Shafi said: (Oct 11, 2012) @Mahantesh, You are correct 3! and 4!, because you spitted vowels and consonants, But to combine them vowels+consonants.i.e. (4 consonants + 1 set of vowels) = 5! And (3 vowels ) = 3! So 5!*3! = 5x4x3x2x1x3x2x1=720.

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Adhityasena said: (Feb 9, 2013) I get the answer to be 2*720. Because, since the vowels must come together in the word LEADING, which actually has 7 letters, E and A can be taken as one unit, so now we have L, EA, D, I, N, G to be arranged and which can be done in 6! ways. But among E and A there are 2 arrangements namely EA and AE, So the final answer is 2*720. Am I right !

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Chetas said: (Jul 6, 2013) @Adhityasena. You have not considered a vowel ‘I’. ‘EAI’ is to be taken as one unit.

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Sanjay(9776387850) said: (Aug 29, 2013) Hi Guys, at first I tell you how can you know is this permutation or combination. Permutation means arrange(row/column) and Combination means selection(group).i.e. Number and Word are perm. Playing 11 and committee are combi. This is a word so this is perm. You should know the formula that m different objects are alike and n different object are alike if we arrange all the m+n objects such that n objects are always together=(m+1)!*n! Here n = Vowel = 3 and m = Con. = 4. So = (4+1)!*3! = 5!*3!. = 120*6 = 720.

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Chithra said: (Nov 5, 2013) As we known very well that * is consider to be AND, + is consider to be OR. Consider the 1st example 7 men and 6 women problem we taken as (7c3*6c2) + (7c4*6c2) + (7c5). We can also said this as (7c3 AND 6c2) OR (7c4 AND 6c2) OR (7c5). CONDITION -> 5 people need to select. We should take 3 men from 7 men and 2 women from 6 women or other option is to take 4 men from 7 men and 1 women from 6 women. That’s why we are using * at the place of AND, + at the place of OR. Similarly, we need to consider both the consonant AND vowel not consonant OR vowel. So we use 5!*3!.

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Taku Mambo Bellnuisemarbel said: (Nov 29, 2013) Please help me with this; whenever I hear of probability that a variable is being selected what should I think of?

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Amna Fida said: (Dec 3, 2013) How we know that factorial will use here?

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Amnafida said: (Dec 3, 2013) Describe that how we know about here permutation is use?

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Jhansi Sri said: (Feb 7, 2014) Please help me quickly why we take 5!*3!, Why we can’t take 5!+3!.

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Pema said: (Aug 3, 2014) When it comes the question for arrangements, then it is a Permutation Or you all can remember it as keyword “PA” P=permutation and A=arrangement. Likewise, for combination, it is all for selection purpose, remember keyword as “CS” c=combination,s=selection. Then apply formula for each. Easy.

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Baidyanath Jena said: (Nov 7, 2014) When it comes to persons it should be combination.

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Samson said: (Nov 17, 2014) God bless you all for your contribution especially you @Jessie for using the formula to break it down well.

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Ranjeet said: (Nov 19, 2014) Well I am confused. Somewhere n! is done whereas somewhere (n-1)! is used. Can someone explain about it?

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Sagar said: (Dec 26, 2014) Hi friends. We know that formula n!=n (n-1) (n-2).3.2.1. Suppose there n way to choose first element (since there are n elements). After that there are n-1 ways to choose second element because already we choose one element from n elements that’s why we are assuming this way. Similarly n-2 ways to chose the third element.etc it’s going like this. n!=n (n-1). n!=n (n-1) (n-2) if n>2 or equals 2. n!=n (n-1) (n-2) (n-3) if n>3 or equals 3. Hope you understood.

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Shantha said: (Apr 30, 2015) Then how we won’t take E+A+I+(LDNG) = 4.

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Tom said: (May 2, 2015) In what situations we can permutation or combination?

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Riya said: (May 8, 2015) @Tom and @Shantha. Whenever there is a reference to some arrangement it is permutation. Whenever there is a reference to some selection it is combination. The given question requires us to find the number of ways in which the word LEADING can be arranged with the condition that the vowels (EAI) always be together. Thus we need to apply the concept of permutation. Here, since the vowels EAI must always be together we consider it as a single word (EAI). Thus, LDNG (EAI) make a 5 letter word. It can be arranged in 5p5 ways = 5!ways. Now, since EAI can arrange itself in 3p3 or 3! ways, the word LDNG (EAI). Can thus be arranged or PERMUTED in 3!*5! ways = 720 ways.

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Spurthy said: (Jun 24, 2015) All the consonants can also be written as a unit?

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Ajay said: (Aug 17, 2015) In some cases unit’s place, tens place’s and hundred’s place are used what its mean?

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Shrinivas said: (Aug 25, 2015) Hi if two vowels are repeated in same word then will you take it as same or as different?

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Vanmathi said: (Sep 1, 2015) In how many ways LEADING be arranged such a way that atleast two vowels always together?

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Soumya Sengupta said: (Sep 18, 2015) If there is another vowel ‘o’ what should be done like in ‘outstanding’ here a, i, o, u are vowels do we have to consider (aiou) = 1 letter for calculation?

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Palak said: (Sep 18, 2015) In this question won’t the arrangement of non vowels matter and why?

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RAJA said: (Sep 19, 2015) Hai @Soumya. S its 1 letter only. Hope you understand.

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Yonatan said: (Sep 24, 2015) I can’t understand the answer.

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Mukesh said: (Dec 18, 2015) Please anyone help me why repetition is not considered in the current problem?

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Eswaru said: (Feb 3, 2016) Hey dude we have to form 7 letter words from LEADING that means we need to use all the letters at a time. So no repetition are allowed.

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Peter said: (Feb 28, 2016) If at least two vowels always together then what will be the answer for LEADING ?

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Siva said: (Mar 16, 2016) Other than vowels there are only 4 letter then how it s possible to get 5!.

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Brian said: (Jun 2, 2016) Correct me if I’m wrong but, There are 7 letters: L E A D I N G 3 vowels and 5 non-vowels. I got the part where we need to permutate 3 and 5, resulting with 3!*5!. But aren’t there also several other positions that these vowels could be positioned? For Example: AIELDNG is one factor, another factor is LAIEDNG, another factor is LDAIENG. As you can see, the positions of the 3 vowels with each other are the same, and the order of non-vowels in the word is also the same, but I only changed the position of the starting point for the vowel permutations, starting from the first position, to the second, to the third. So, I believe that the answer should be 3!*5!*5. Since there are 5 different ways you could represent the same order of vowels in different positions with the same order of non-vowels. Please do correct me if I’m wrong or if I misunderstood the question

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Technothelon said: (Jun 9, 2016) @Brian. There aren’t such kind of ways. Because arrangement is not taken into consideration when we do combinations.

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KIRUPA RANI D said: (Jun 29, 2016) Can you give solution for this problem? How many words can be formed from the letters of the word ‘PACKET’, so that the vowels are never together?

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Jomson Joy said: (Aug 3, 2016) In PACKET there are 2 vowels. Vowels came 2gether means 4! * 2! = 240. Total words formed =6! (because of total letters) = 720. Therefore 720 – 240 = 480.

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Gopika S S said: (Aug 3, 2016) A number of permutations of “n” different things are taken “m” specified things always come together is m!* (n-m+1) ! Here the three vowels always come together. So here m is 3. A total number of letters is 7. Substitute we get.3!* (7 – 3 + 1)! = 3! * 5! = 6 * 120 =720. Hope you got it.

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Prajwal said: (Aug 17, 2016) Does it have an another method to find the solution?

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Rakesh said: (Sep 16, 2016) In leading 5! * 3! ways we can fill all vowels come together.

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Otieno said: (Nov 30, 2016) Where has 5! come from? Please explain me.

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Xyz said: (Dec 20, 2016) How many letters can be formed from COMBINATION if vowels are kept together? Please give the solution.

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Sowmya said: (Dec 23, 2016) @Xyz. C,M,B,N,T,N,(O,I,A,I,O)=> C,M,B,T,N,(O,I,A)=> 6! ways. Vowels alone can be rearranged themselves in 3! ways. So 6! * 3! = 2160. Hope this is right.

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Navan said: (Feb 2, 2017) I have one question. How many ways 11players selected from 15 players? Please give me the answer.

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Akshay said: (Mar 31, 2017) @Navan.15c11 = 15!&div(15-11)! * 11!

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Avishek Kadel said: (Apr 21, 2017) In how many ways the letters of word ELEMENT can be arranged so that vowels are always together? Can anyone solve this?

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Ali said: (Apr 26, 2017) @Avishek No. of vowels is 3Es and the can only be together in this pattern, There is only 1 way of choosing so 1! = 1 * 1 = 1. We are to consider 3Es as a single alphabet because they are together. So we have L, M, N, T, ie 5 letters now in all. Now of way of choosing 5 letters = 5! (5 * 4 * 3 * 2 * 1) = 120. Finally, we multiply 120 * 1 = 120 ie. the number of ways of arranging the letters so that the vowels are always together.

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Krishna said: (May 23, 2017) LEADING- vowels together in total 5 positions at L, E, A, D, and I. Ex. For the first position – (EAI) – (remaining 4 lettersLNGD) – 4! * 3! For total 5 positions – 5*3!*4! -720.

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Abhishek said: (Jul 18, 2017) I think it should be 3!*4!

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Tanmay said: (Aug 14, 2017) In how many different ways can the letters of the word software be arranged in such a way that the vowels always come together?

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Jon said: (Aug 17, 2017) @Tanmay. SFTWR (OAE) 5 +(1) ! = 6! OAE can be arranged in 3 ways 3! 6! = 6*5*4*3*2*1 = 720 ways 3! = 6 ways 720*6 = 4320 ways!

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Dhana said: (Oct 9, 2017) Word : leading condition : vowels together eai-3! ldng&eai-5! (ldng)&(eai)-2! Whether the last condition is valid? Give explanation.

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Nabin Shah said: (Nov 5, 2017) Why do 120 and 6 multiply?

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Vivek Sharma said: (Nov 11, 2017) It should be 1440, as the vowels can be after the consonants as well as before the consonants. So 720*2. Am I right?

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Heta Vaghasia said: (Nov 12, 2017) Answer will be 72. How 720 came?

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DragonSlayer said: (Jan 15, 2018) Friends in the word LEADING. there are three vowels A,E,I With AEI you can form 3! arrangements ie 6 arrangements As we want the vowels to come together they may be placed at any of the 5 locations on the word LEADING. So there are 5! arrangements for this.5! X 3!=720. The 3 vowels are considered as a single word to simply this process of counting the number if locations.

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Juliana said: (Mar 14, 2018) How do you calculate combinations, can you do an example? Please.

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Saravanakumar said: (Apr 6, 2018) LEADING. Total vowels : E, A, I remaining : LDNG assume : EAI we can arrange (EAI)L, L(EAI), D(EAI), N(EAI),G(EAI) so, total remaining is 4 so, 5! and possibilities of arranging refer “assume”, 3! then answer is : 5!*3! 120 * 6=720.

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Shivam said: (May 23, 2018) Why 120*6 why not 120+6? Please explain me.

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Sankardev said: (Jun 10, 2018) -L-D-N-G.5!/(5-3)! = 120/2=60.60*3!=60*6, =360.

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Supriya said: (Jun 22, 2018) LEADING- V-3,(1 unit). C-4,(4+ 1unit)=5! n-7. =5!*3!=120*6=720.

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Tushar said: (Oct 25, 2018) @Shiva. It means 5!.

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Pooja said: (Dec 31, 2018) 5! means? Explain

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Kiran Kumar K said: (Apr 5, 2019) How you get 5(4+1=5) i.e 5!?

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Adhi said: (May 22, 2019) Will anyone please explain, how can arrange if one more same vowels had. Eg CORPORATION?

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Aniket Arsad said: (Jun 13, 2019) Vowels are EA so _L_D_I_N_G_. So there is six space we can arrange EA so the answer is 6! = 720.

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Pallavi said: (Jun 14, 2019) Why 120*6? Why not 120+6? Please tell me the reason.

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Ameena said: (Aug 2, 2019) Hello, We have word leading.we have vowels( EAI), first taken as 1 and can be arranged in _L_D_N_G_ that is in 5! Ways, EAI in 3! Ways, and LNDG in 4! ways. That is 5! * 4! * 3! = 17,280 ways.

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Deepanesh said: (Aug 21, 2019) Why we are taking possibilities of vowels too?

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Aradhy said: (Sep 22, 2019) @Deepanesh. We are taking the possibilities of vowel because vowels can also change their position in the given arrangement.

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Suraj said: (Oct 28, 2019) Make a queue of vowels should not come together.

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Xyz said: (Nov 30, 2019) How many 5 letter words can be formed out of the word NATIONALIST? How to solve this. Please help!

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Keerti AR said: (Jun 14, 2021) LEADING = 7 letters => 4 alphabets (LNDG) + 1 group (3 vowels) = 5 ! ways. =>5 * 4 * 3 * 2 * 1 = 120. Now, the group can be arranged in 3 ways, since there are 3 vowels, So 3!=6 (3 * 2 * 1). Hence, 120 * 6 = 720 ways can be arranged.

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DHEEPAK S said: (Jul 26, 2021) I can’t understand this, Please anyone help me to get it.

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Sanjay Raj G said: (Feb 2, 2022) @All. Answer is not 720. Ans is 5040. L E A D I N G Total 7! So 1*2*3*4*5*6*7 = 5040.

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Ayush said: (Feb 4, 2022) Here 5! = 5*4*3*2*1 = 120.

Aptitude – Permutation and Combination – Discussion
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How many vowels are there in school?

– As we mentioned before, there are 5 different vowel letters in the English language. These are ‘a’, ‘e’, ‘i’, ‘o’ and ‘u’. In some cases, ‘y’ and ‘w’ can be considered vowels. We’ll explain a bit more about that later! And what’s more, the sounds that the vowels make often fall into one of two main groups: short vowel sounds and long vowel sounds.

Words that contain short vowels include: bat, cat, bed, leg, but, bug, bog, hip, pop and sip. Words that contain long vowels include: haze, he, she, hope, human, cute and equal.

As you might have guessed from these examples, the way to tell if a vowel sound is long or short is whether it sounds the same as the name of its letter!
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How many methods of education are there?

HANDOUT 9. TYPES OF TEACHING METHODS – There are different types of teaching methods which can be categorised into three broad types. These are teacher-centred methods, learner-centred methods, content-focused methods and interactive/participative methods.

A) INSTRUCTOR/TEACHER CENTRED METHODS Here the teacher casts himself/herself in the role of being a master of the subject matter. The teacher is looked upon by the learners as an expert or an authority. Learners on the other hand are presumed to be passive and copious recipients of knowledge from the teacher.

Examples of such methods are expository or lecture methods – which require little or no involvement of learners in the teaching process. It is also for this lack of involvement of the learners in what they are taught, that such methods are called “closed-ended”.

• B) LEARNER-CENTRED METHODS In learner-centred methods, the teacher/instructor is both a teacher and a learner at the same time.
• In the words of Lawrence Stenhouse, the teacher plays a dual role as a learner as well “so that in his classroom extends rather than constricts his intellectual horizons”.
• The teacher also learns new things everyday which he/she didn’t know in the process of teaching.

The teacher, “becomes a resource rather than an authority”. Examples of learner-centred methods are discussion method, discovery or inquiry based approach and the Hill’s model of learning through discussion (LTD). (c) CONTENT-FOCUSED METHODS In this category of methods, both the teacher and the learners have to fit into the content that is taught.

Generally, this means the information and skills to be taught are regarded as sacrosanct or very important. A lot of emphasis is laid on the clarity and careful analyses of content. Both the teacher and the learners cannot alter or become critical of anything to do with the content. An example of a method which subordinates the interests of the teacher and learners to the content is the programmed learning approach.

(d) INTERACTIVE/PARTICIPATIVE METHODS This fourth category borrows a bit from the three other methods without necessarily laying emphasis unduly on either the learner, content or teacher. These methods are driven by the situational analysis of what is the most appropriate thing for us to learn/do now given the situation of learners and the teacher. Teacher-centred methods Learner centred methods Content focused methods Interactive/participative methods SPECIFIC TEACHING METHODS We can now consider a number of specific methods which can be drawn from in the course of classroom instruction. It is however, important to note that the choice of any form of methods should not be arbitrary, but needs to be governed by the criteria we have already examined.

At the same time each method is not fool-proof, but has its own advantages and disadvantages. That is why I would recommend the use of complementary methods rather than one method.1. LECTURE METHOD A lecture is an oral presentation of information by the instructor. It is the method of relaying factual information which includes principles, concepts, ideas and all THEORETICAL KNOWLEDGE about a given topic.

In a lecture the instructor tells, explains, describes or relates whatever information the trainees are required to learn through listening and understanding. It is therefore teacher-centred. The instructor is very active, doing all the talking. Trainees on the other hand are very inactive, doing all the listening.

Despite the popularity of lectures, the lack of active involvement of trainees limits its usefulness as a method of instruction. The lecture method of instruction is recommended for trainees with very little knowledge or limited background knowledge on the topic. It is also useful for presenting an organised body of new information to the learner.

To be effective in promoting learning, the lecture must involve some discussions and, question and answer period to allow trainees to be involved actively. PREPARATION AND DELIVERY OF A LECTURE As stated earlier, during the lecture, the trainees merely listen to the instructor.

1. It is therefore very important to consider the attention span of trainees when preparing a lecture.
2. The attention span is the period of time during which the trainees are able to pay full attention to what the instructor is talking about.
3. It is estimated to be 15-25 minutes only.
4. It is difficult to hold the trainees attention for a long period of time and careful preparation of lectures is very necessary.

The instructor should have a clear, logical plan of presentation. He/she should work out the essentials of the topic, organise them according to priorities and logical connections, and establish relationships between the various items. Careful organisation of content helps the trainees to structure and hence, to store or remember it.

When developing a theme in a lecture, the instructor should use a variety of approaches. A useful principle in any instruction is to go from the KNOWN to UNKNOWN ; from SIMPLE to COMPLEX, or from PARTS to a WHOLE, Knowing the trainees and addressing their needs and interests is very important. For example, in explaining technical processes the instructor should search for illustrations that will be familiar to the trainees.

Unfamiliar technical words should be introduced cautiously. New terminologies should be defined and explained and examples given. In order to gain and focus the attention of trainees, the instructor should be adequately prepared, fluent in his/her presentation and should use various teaching aids and illustrations such as charts, transparencies, codes and even the real objects during presentation.

Question and Answer periods should be included in the lecture. QUALITIES OF A GOOD LECTURE 1. A good lecture should not be too long as to exceed the trainees attention span (up to 25 minutes).2. A good lecture should address a single theme.3. In a good lecture technical terms are carefully explained.4. Familiar examples and analogies are given.5.

A good lecture establishes fluency in technical content.6. A good lecture uses illustrations and examples.7. A good lecture builds on existing knowledge.8. A good lecture employs a variety of approaches.2. THE DISCUSSION METHOD Discussion involves two-way communication between participants.

1. In the classroom situation an instructor and trainees all participate in discussion.
2. During discussion, the instructor spends some time listening while the trainees spend sometimes talking.
3. The discussion is, therefore, a more active learning experience for the trainees than the lecture.
4. A discussion is the means by which people share experiences, ideas and attitudes.

As it helps to foster trainees involvement in what they are learning, it may contribute to desired attitudinal changes. Discussion may be used in the classroom for the purpose of lesson development, making trainees apply what they have learnt or to monitor trainees learning by way of feedback.

• LESSON DEVELOPMENT In areas in which trainees already have some knowledge or experience, discussion may be used to develop the main points to be covered in a lesson.
• For example, in safety training many of the procedures and behaviour that should be observed can be established through discussion with trainees.

Trainees can draw on their experience of working in workshops contract sites to contribute to the discussion. In discussing some issues, differences of opinion arise. The discussion can help to clarify the different points of view and may assist each trainee to define his or her own opinion.

Used in this way, discussion may be more effective in motivating trainees than lectures. Trainees can see that some importance is attached to their contributions. APPLICATION Discussion may also be used, following a lecture or demonstration, to help trainees apply what they have learned. The instructor can ask questions, that help trainees to relate concepts and principles to contexts that are familiar to the trainees or in which they will ultimately be needed.

For example following a lecture on “types of wood joint”, the instructor may, lead a discussion directing trainees attention to the places or pieces of furniture where each type is found, and the reasons for using one type than the other. Used in this way discussion contributes to the transfer of learning.

1. FEEDBACK The discussion method also provides an opportunity to monitor trainees learning.
2. The answers provided by trainees and the questions they ask, reveal the extent and quality of learning taking place.
3. Instructors can use this information to repeat or modify an explanation to improve learning.
4. They can also provide feedback to trainees, thereby helping to reinforce learning that has taken place.

Discussion used in this way should follow after other methods of classroom instruction such as lectures, demonstration or practice sessions. CONDUCTING A DISCUSSION Discussion sessions can be led by the instructor, or can take place in groups. In either case, the goal is to meet the lesson objectives by allowing the trainees to:- a) Relate relevant personal experiences or events which have occurred in the work setting.

1. B) Contribute ideas or personal opinions.
2. C) Apply what has been learned to familiar situations or solving problems.
3. D) Express what had been learned.
4. Whether the discussion is instructor led or takes place in groups it must be guided by the instructor.
5. It must be focused on the objectives of the lesson: it is the instructors responsibility to see that the objectives are met.

If it is not properly guided, a discussion can degenerate into a consideration of inappropriate or unimportant topics adding confusion rather than clarification to the lesson.3. THE DEMONSTRATION LESSON “The most effective way to teach an occupational skill is to demonstrate it.

• One of the two most essential teaching skills is the ability to demonstrate; the other is the ability to explain.
• Both are vital to the success of either an operation lesson or an information lesson”.
• Weaver and Cencil in APPLIED TEACHING TECHNIQUES,
• DEFINITION Demonstration means any planned performance of an occupation skill, scientific principle or experiment.

TEACHER PREPARATION 1. Rehearse your presentation in advance of the lesson.2. Anticipate any difficult steps, possible interruptions e.t.c.3. Obtain all materials, tools, equipment, visual and teaching aids in advance and check their useful condition.4.

Have all materials within reach and conveniently arranged.5. Time the demonstration NOT to exceed 15 minutes.6. Remove all extraneous materials; check lighting, visibility, student grouping, and proximity to electric, gas and water outlets.7. Plan to use a skill or method to advantage; work from simple to complex, one step at a time.

PRESENTATION 1. Make sure all students can see and hear the lesson.2. Be enthusiastic, professional, effective but not dramatic.3. Relax; use any mishaps or humour to YOUR advantage.4. Observe all safety rules and procedures.5. Keep eye-contact with the class; ask and encourage class questions.6.

Explain WHY and HOW: use the techniques of SHOW and TELL.7. Use a medial summary to strengthen your explanation. PRECAUTIONS 1. Avoid interruptions; keep demonstration smooth and continuous.2. Never demonstrate on a student’s material.3. Work towards one aim.4. Allow time for possible student participation.

CARRYING OUT A DEMONSTRATION 1. Give a good performance. Remember that the trainees learn by your good example.2. Explain each step or process as you proceed. Follow your lesson plan.3. Make sure the trainees see the demonstration from the angle they will perform it themselves.4.

1. Be sure everyone can see and hear.
2. Maintain eye contact.5.
3. Emphasise key points, and if possible prepare before hand ask key questions as you go along and allow trainees to ask questions.6.
4. Observe all safety rules, precautions and procedures; and emphasise them.7.
5. Use proper instructions, aids such as chalkboard, charts, handouts e.t.c.

to support your demonstration.8. Provide for trainees participation where possible, during and after demonstration.9. Demonstrate the correct way only. First impressions are important, therefore, make them correct ones.10. Always summarise the steps and emphasise key points again.

AFTER DEMONSTRATION 1. Return all items used during demonstration to their storage places.2. Make arrangements to have the trainees practice the skill as soon as possible in a practical class session.3. Observe and analyse trainee(s) performance and correct mistakes.4. Offer reinforcement where necessary.5.

Coach weak or slow trainees.6. Check trainee’s completed work for accurate performance and record.7. Allow sufficient time interval before demonstrating another operation.4. BUZZ GROUPS Another method of instruction is the buzz group. During a longer session, the plenary group can break into sub-groups to discuss one or two specific questions or issues.

The room soon fills with noise as each sub-group ‘buzzes’ in discussion. If appropriate, after the discussion one member of each group can report its findings back to the plenary. Buzz groups can be in pairs, trios, or more depending on the activity. People turn to their neighbours for a quick buzz, or form larger groups of three or more.

This allows almost every one to express an opinion. While they are buzzing, participants are able to exchange ideas and draw on their wide collective experience. It may provide a good opportunity for trainees to reflect on the content of a lecture. A good buzz session will generate many ideas, comments and opinion, the most important of which will be reported back.

Buzzgroups help trainers as they allow you to: – Draw your breath – Gauge the mood, by listening to some of the discussions – Change pace of the session – Encourage participants to reflect on what they have learnt and how they might apply it in their work. DISADVANTAGES The main obstacle using buzz sessions lie in unfamiliarity with their use, the time required, the need for leaders or facilitators within each sub-group, and the need to have tables and chairs arranged for quick and easy discussion.5.

BRAINSTORMING The purpose of a brainstorming session is to discover new ideas and responses very quickly. It is particularly a good way of getting bright ideas. It differs from the buzz groups discussion in that the focus is on generating as many ideas as possible without judging them.

In this technique, all ideas are given equal credence. Participants are encouraged to let ideas flow freely, building on and improving from previous ideas. No idea, however crazy, should be rejected. These ideas are listed exactly as they are expressed on a board or flipchart, or written on bits of paper.

The combination of swiftly generated ideas usually leads to a very animated and energising session. Even the more reserved participants should feel bold enough to contribute. The purpose of listing responses is to collect existing experiences and thoughts.

It is useful to collect answers to questions when you expect much repetition in the responses. After a brainstorm session, the ideas can be discussed further and evaluated, for example listing the best options in a systematic way. Ideas can be grouped and analysed so that they belong to the group rather then individuals.

Unlike a buzz session, a brainstorm session can work well with a large group and usually takes less time. It is best to limit the time for plenary brainstorms, as you might lose the attention of some participants.6. ROLE PLAYS In role plays, participants use their own experiences to play a real life situation.

• When done well, role plays increase the participants self-confidence, give them the opportunity to understand or even feel empathy for other people’s viewpoints or roles, and usually end with practical answers, solutions or guidelines.
• Role plays are useful for exploring and improving interviewing techniques and examining the complexities and potential conflicts of group meetings.

They help participants to consolidate different lessons in one setting and are good energisers. However, role plays can be time-consuming and their success depends on the willingness of participants to take active part. Some trainees may feel a role play is too exposing, threatening or embarrassing.

This reluctance may be overcome at the outset by careful explanation of the objectives and the outcome. Some role plays can generate strong emotions amongst the participants. It is therefore essential that a role play is followed by a thorough debriefing. This provides the opportunity for the trainer and the participants to raise and assess new issues.

INSTRUCTIONAL METHODS AND THEIR APPLICATIONS

METHOD	USES	ADVANTAGES	DISADVANTAGES
THE LECTURE METHOD A formal or semi-formal discourse is which the instructor presents a series of events, facts, or principles, explores a problem or explains relationships	1. To orient students.2. To introduce a subject.3. To give directions on procedures.4. To present basic material.5. To introduce a demonstration, discussion, or performance.6. To illustrate application of rules, principles, or concepts.7. To review, clarify, emphasise or summarise.	1. Saves time.2. Permits flexibility.3. Requires less rigid space requirement.4. Permits adaptability.5. Permits versatility.6. Permits better centre over contact and sequence.	1. Involves one way communication.2. Poses problems in skill teaching.3. Encourages student passiveness.4. Poses difficulty in gauging student reaction.5. Require highly skilled instructors.
THE DISCUSSION METHOD A method in which group discussion techniques are used to reach instructional objectives.	1. To develop imaginative solutions to problems.2. To stimulate thinking and interest and to secure student participation.3. To emphasise main teaching points.4. To supplement lectures, reading, or laboratory exercises.5. To determine how well student understands concepts and principles.6. To prepare students for application of theory of procedure.7. To summarise, clarify points or review.	1. Increase students interest 2. Increases students acceptance and commitments.3. Utilises student knowledge and experience.4. Results in more permanent learning because of high degree of student participation.	1. Require highly skilled instructor.2. Requires preparation by student.3. Limits content.4. Consumes time.5. Restricts size of groups.
THE PROGRAMMED INSTRUCTION METHOD A method of self-instruction	1. To provide remedial instruction.2. To provide make-up instruction for late arrivals, absentees, or translents.3. To maintain previously learned skills which are not performed frequently enough.4. To provide retraining on equipment and procedures which have become obsolete.5. To upgrade production.6. To accelerate capable students.7. To provide enough common background among students.8. To provide the review and practice of knowledge and skills.	1. Reduce failure rate.2. Improves end-of-course proficiency.3. Saves time.4. Provides for self instruction.	1. Require local or commercial preparation.2. Requires lengthy programmer training.3. Increases expenses.4. Requires considerable lead time.
THE STUDY ASSIGNMENT METHOD A method in which the instructor assigns reading to books, periodicals, project or research papers or exercises for the practice.	1. To orient students to a topic prior to classroom or Laboratory work.2. To set the stage for a lecture demonstration or discussion.3. To provide for or capitalise on individual differences in ability, background, or experience through differentiated assignments.4. To provide for the review of material covered in class or to give practice.5. To provide enrichment material.	1. Increase coverage of material.2. Reduce classroom time.3. Permits individual attention.	1. Require careful planning and follow up.2. Poses evaluation problem.3. Produce non-standard results.
THE TUTORIAL METHOD A method of instruction in which an instructor works directly with an individual student.	1. To reach highly complicated skills operations or operations involving danger or expensive equipment.2. To provide individualised remedial assistance.	1. Permits adaptive instruction.2. Stimulates active participation.3. Promotes safety.	1. Requires highly competent instructor.2. Demands time and money.
THE SEMINAR METHOD A tutorial arrangement involving the instructor and groups, rather than instructor and individual.	1. To provide general guidance for a group working on an advanced study or research project.2. To exchange information on techniques and approaches being explored by members of a study or research group.3. To develop new and imaginative solutions to problems under study by the group.	1. Provides motivation and report.2. Stimulates active participation.3. Permits adaptive instruction.	1. Requires highly competent instructor.2. Poses evaluation problems.3. Is more costly than most other methods.
THE DEMONSTRATION METHOD A method of instruction where the instructor by actually performing an operation or doing a job shows the students what to do, how to do it, and through explanations brings out why, where, and when it is done.	1. To teach manipulative operations or procedures.2. To teach troubleshooting.3. To illustrate principles.4. To teach operation or functioning of equipment.5. To teach teamwork.6. To set standards of workmanship.7. To teach safety procedures.	1. Minimise damage and waste 2. Saves time 3. Can be presented to large groups.	1. Require careful preparation and rehearsal.2. Requires special classroom arrangements.
THE DEMONSTRATION METHOD A method of instruction is required to perform under controlled conditions the operations, skills or movement being taught.	1. To teach manipulative operations or procedures.2. To teach operation or functioning of equipment.3. To teach team skills 4. To teach safety procedures.	1. Builds confidence.2. Enable learning evaluation.3. Reduces damages and waste.4. Promotes safety.	1. Requires tools and equipment.2. Requires large block.3. Requires more instructors.
THE BUZZ GROUP	1. To develop and express imaginative ideas, opinions.2. Stimulate thinking.	1. Help trainers to draw breath.2. Gauge the mood by listening to some discussion.3. Change pace of discussion.4. Encourage participants to reflect what was learnt.	1. Unfamiliarity in use.2. Time required.3. Need for group leaders.
BRAINSTORMING	1. Discover new ideas, thoughts and responses very quickly.	1. Leads to a very animated and energising session.2. More reserved participants feel free to contribute.	1. It takes time particularly if it is a large group.2. May consume a lot of material e.g. flipcharts or writing materials.3. Requires high level facilitation skills.
ROLE PLAYS	1. Exploring and improving interviewing techniques and examining complexities and potential conflicts of groups.2. To consolidate different lessons in one setting.	1. Good energizers.2. Promotes empathy of trainees for other situation.3. Encourrages creativity in learning.	1. Participants might be reluctant.2. May not work with trainees who do not know each other well.

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How many syllables are in education?

Education = ed/u/ca/tion ( four syllables are present in it.
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What is the base word of education?

Bass, Randall V.; Good, J.W. Educational Forum, The, v68 n2 p161-168 Win 2004 Craft (1984) noted that there are two different Latin roots of the English word “education.” They are “educare,” which means to train or to mold, and “educere,” meaning to lead out.

1. While the two meanings are quite different, they are both represented in the word “education.” Thus, there is an etymological basis for many of the vociferous debates about education today.
2. The opposing sides often use the same word to denote two very different concepts.
3. One side uses education to mean the preservation and passing down of knowledge and the shaping of youths in the image of their parents.

The other side sees education as preparing a new generation for the changes that are to come-readying them to create solutions to problems yet unknown. One calls for rote memorization and becoming good workers. The other requires questioning, thinking, and creating.

• To further complicate matters, some groups expect schooling to fulfill both functions, but allow only those activities promoting educare to be used.
• Balance in educational aims is a valid focus for educators.
• This author contends that, in order to achieve balance, educators must start by changing the organizational structure or the ways in which decisions are made.

Utilizing stakeholder perceptions in determining aims, establishing a shared vision of education, and facilitating a change in educators’ roles are initial steps. To accomplish a change in thinking, educators must examine their own personal mastery and mental models of education.
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What word has all 5 vowels?

List of Vowel Words in English – In the English language, there are various words that are made of only vowels and there are some words that are made up of all the five vowels. Below in this article, we have provided a list of words that contain all the five vowels in them. Check the list of words with all vowels in them.

Education	Automobile	Evacuation
Remuneration	Regulation	Misbehaviour
Authorities	Authorise	Authentication
Precaution	Miraculousness	Misdemeanour
Perambulation	Auriferous	Mensuration
Tambourine	Unostentatious	Unobjectionable
Multimillionaire	Consequential	Precarious

EUNOIA is the shortest word in English which has all five vowels. Scream, dream, clean, spoil, encyclopaedia, onomatopoeia, bouquet, queue, etc. are some words which have vowels in a row. : Vowel Words: Check the Words Containing All the Vowel Letters
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What word has 7 vowels in a row?

The Five Vowels – The shortest word containing all five vowels exactly once is the six-letter EU N OIA, meaning alertness of mind an will (and also the title of a book by Canadian poet Christian Bok). However, it is not included in any major English dictionary.

There are several seven-letter words containing all the vowels, including S E Q UOIA, EU L O G IA, M IAOUE D, A D OU L IE, EU C O S IA, EU N O M IA, EU T O P IA, M OI N EAU, and D OU L EIA, The relatively common French word OI S EAU (meaning bird) contains all five vowels, once each. The shortest word with the five vowels occurring in alphabetical order is AE R IOU S (airy), which has seven letters.

The longest such word is PHR A G E LL IO RHYNCH U S (a protozoan) with 18 letters. There are two seven-letter words in Portuguese that contain the five vowels in alphabetical order: A C EI T OU and A L EI J OU, S UOI D EA (the taxonomic group to which pigs belong) is the shortest word with the five vowels in reverse alphabetical order.

• The longest such word is P U NCT O SCHM I DT E LL A (a crustacean).
• U LTR A R E V O L U T IO N A R IE S has each vowel exactly twice.
• The shortest such word is C U B OI D EO N A V I C U L A R E, and the longest, U SS O LZ E W IE CH I N O G A MM A R U S (a small crustacean).
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