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Updated on: 08 Jul 2015, 08:04
Originally posted by GMATinsight on 08 Jul 2015, 07:41.
Last edited by Bunuel on 08 Jul 2015, 08:04, edited 1 time in total.
Last edited by Bunuel on 08 Jul 2015, 08:04, edited 1 time in total.
Renamed the topic and edited the question.
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
78% (01:44) correct
22%
(02:03)
wrong
based on 172
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History
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Time
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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!
A) 9!
B) 5!*4!
C) 5!*5!
D) 5!*4!*2!
E) 6!*4!
ENGRTOMBA2018
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
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Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
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08 Jul 2015, 07:50
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GMATinsight
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.
08 Jul 2015, 11:30
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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,
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,
