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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
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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!

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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.
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 11 Jul 2015, 08:19
1
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)
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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 11 Jul 2015, 08:45
GMATinsight wrote:
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!


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.
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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 17 Nov 2016, 20:23
Treat vowels like a unit and consonants like a unit --> We know the blocks could be arranged in two ways (1)

(2) Number of ways vowels can be arranged --> 5!

(3) Number of ways consonants can be arranged --> 4!

(1)(2)(3) = 2x5!x4!

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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 17 Nov 2016, 20:23
Treat vowels like a unit and consonants like a unit --> We know the blocks could be arranged in two ways (1)

(2) Number of ways vowels can be arranged --> 5!

(3) Number of ways consonants can be arranged --> 4!

(1)(2)(3) = 2x5!x4!

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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 29 Nov 2016, 16:38
1
GMATinsight wrote:
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!


We need to determine the number of ways to arrange the letters of word "EDUCATION" such that all the vowels as well as all the consonants always appear together. We start by arranging the given word with vowels together with the consonants together.

[EUAIO] [DCTN]

We first see that there are 2 ways to arrange [EUAIO] and [DCTN]: [EUAIO] [DCTN], [DCTN] [EUAIO].

Next we must determine the number of arrangements for the letters in [EUAIO] and in [DCTN].

[EUAIO] can be arranged in 5! ways.

[DCTN] can be arranged in 4! ways.

Thus, the total number of ways to arrange the letters of word "EDUCATION" such that all the vowels as well as all the consonants always appear together is 5! x 4! x 2, or 5! x 4! x 2!.

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

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Re: In how many ways can the letters of word "EDUCATION" be arranged such   [#permalink] 23 Oct 2019, 03:13
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