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In how many ways can the letters of the word MAXIMA be arran

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In how many ways can the letters of the word MAXIMA be arran [#permalink]  14 May 2019, 00:35
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Question Stats:

76% (01:12) correct 23% (02:05) wrong based on 13 sessions
In how many ways can the letters of the word MAXIMA be arranged such that all vowels are together?

(A) 12

(B) 18

(C) 30

(D) 36

(E) 72
[Reveal] Spoiler: OA

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Re: In how many ways can the letters of the word MAXIMA be arran [#permalink]  22 Aug 2019, 19:07
Carcass wrote:
In how many ways can the letters of the word MAXIMA be arranged such that all vowels are together?

(A) 12

(B) 18

(C) 30

(D) 36

(E) 72

I believe the answer to this one is 18.

there are double letters in both so we can write them in form ABB. Which has 3 forms.
We can also put either vowels or consonants first (2 more combinations)

Thus we have
2*3*3 = 18

So B.
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Re: In how many ways can the letters of the word MAXIMA be arran [#permalink]  28 Sep 2019, 04:01
Separating all vowels: AAI
Separating all consonants: MXM

These 2 groups can be arranged in 2! ways.

Each group can now be arranged in 3!2!3!2! ways

So total number of ways is 2!∗3!2!∗3!2!2!∗3!2!∗3!2!

= 18

option: B
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Re: In how many ways can the letters of the word MAXIMA be arran [#permalink]  01 Oct 2019, 11:37
Vowel letters have to be together. So possible arrangements,

_ _ _ _ => E.g 1 occurence M AIA X M

As, M has been repeated twice this can be arranged in 4!/2! ways ((total number of letters)!/(number of repeats)!)
Similarly for each of the (4!/2!) ways, AIA can be arranged in (3!/2!) ways ---> Permutation for repeated items
So,
It can be arranged in (4!/2!)*(3!/2!) = 36
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Re: In how many ways can the letters of the word MAXIMA be arran [#permalink]  01 Oct 2019, 11:43
logann2 wrote:
Carcass wrote:
In how many ways can the letters of the word MAXIMA be arranged such that all vowels are together?

(A) 12

(B) 18

(C) 30

(D) 36

(E) 72

I believe the answer to this one is 18.

there are double letters in both so we can write them in form ABB. Which has 3 forms.
We can also put either vowels or consonants first (2 more combinations)

Thus we have
2*3*3 = 18

So B.

It has not been mentioned that the consonants have to together too.
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Re: In how many ways can the letters of the word MAXIMA be arran [#permalink]  01 Oct 2019, 14:28
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Re: In how many ways can the letters of the word MAXIMA be arran   [#permalink] 01 Oct 2019, 14:28
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