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Updated on: 08 Jul 2015, 08:05
Originally posted by GMATinsight on 08 Jul 2015, 07:39.
Last edited by Bunuel on 08 Jul 2015, 08:05, edited 1 time in total.
Last edited by Bunuel on 08 Jul 2015, 08:05, edited 1 time in total.
Renamed the topic and edited the question.
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In how many ways can the letters of word "EDUCATION" be arranged such that all the vowels as well as all the Consonants always 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!
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11 Jul 2015, 08:19
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Since all the vowels and consonants have to be together there can only be there are 5! way to order the vowels and 4! to order the consonants. But they must be together either vowels come first or consonants so you multiply by 2.
So 5!4!2! (D)
So 5!4!2! (D)
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11 Jul 2015, 08:45
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GMATinsight
In how many ways can the letters of word "EDUCATION" be arranged such that all the vowels as well as all the Consonants always 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!
EDUCATION has 5 vowels and 4 consonants. Thus per the question, we can have the following arrangement: VVVVVCCCC
Treating all vowels as 1 group and all consonants as 1 group, we get V C and this can be arranged in 2! ways. Also, the entire vowel group can be arranged in 5! ways (as all the vowels are different or as 5P5 = 5!). Similarly, the entire consonant group can be arranged in 4! ways (as all of them are different).
Thus, the total number of arrangements = 5!*4!*2! . Thus D is the correct answer.
