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In how many ways can the letters of word "EDUCATION" be arranged such

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In how many ways can the letters of word "EDUCATION" be arranged such  [#permalink]

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New post Updated on: 08 Jul 2015, 08:05
1
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A
B
C
D
E

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  45% (medium)

Question Stats:

60% (01:06) correct 40% (01:21) wrong based on 70 sessions

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In how many ways can the letters of word "EDUCATION" be arranged such that all the vowels always appear together?

A) 9!
B) 5!*4!
C) 5!*5!
D) 5!*4!*2!
E) 6!*4!

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Originally posted by GMATinsight on 08 Jul 2015, 07:35.
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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Re: In how many ways can the letters of word "EDUCATION" be arranged such  [#permalink]

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New post 08 Jul 2015, 07:45
GMATinsight wrote:
In how many ways can the letters of word "EDUCATION" be arranged such that all the vowels always appear together?

A) 9!
B) 5!*4!
C) 5!*5!
D) 5!*4!*2!
E) 6!*4!


Let the arrangment be: _ _ _ _ _ _ _ _ _ _ (9 letters, 5 vowels a,e,i,o,u and 4 consonants d,c,t,n)

For all vowels together, consider them as 1 group {a,e,i,o,u}, d,c,t,n --> this gives us 5! arrangements with {} group considered as 1 . Now {} group can in itself be arranged in 5! ways
Thus total arrangements with all consonants together = 5!*5! --> C is the correct answer.
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Re: In how many ways can the letters of word "EDUCATION" be arranged such   [#permalink] 08 Jul 2015, 07:45
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