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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, 00:36
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In how many ways can the letters of the word MAXIMA be arranged such that all vowels are together and all consonants are together?

(A) 12

(B) 18

(C) 30

(D) 36

(E) 42
[Reveal] Spoiler: OA

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Director
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Re: In how many ways can the letters of the word MAXIMA be arran [#permalink]  12 Aug 2019, 05:32
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Re: In how many ways can the letters of the word MAXIMA be arran [#permalink]  12 Aug 2019, 07:23
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Carcass wrote:
In how many ways can the letters of the word MAXIMA be arranged such that all vowels are together and all consonants are together?

(A) 12

(B) 18

(C) 30

(D) 36

(E) 42

Here,

Let arrange the words in vowels and consonants

Vowels:: AIA

consonants : MXM

Vowels can be arranged in = $$\frac{(3!)}{(2!)} = 3$$ (it is divided by 2! since vowel A repeats twice)

Similarly, consonants can be arranged = $$\frac{(3!)}{(2!)} = 3$$ (it is divided by 2! since consonants I repeats twice)

Now, these arrangement can be arranged in 2 ways::

V V V C C C
OR
C C C V V V

Hence, the number of ways it can be arranged = $$2 * 3 * 3 = 18$$ ways
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Re: In how many ways can the letters of the word MAXIMA be arran [#permalink]  22 Aug 2019, 16:53
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Carcass wrote:
In how many ways can the letters of the word MAXIMA be arranged such that all vowels are together and all consonants are together?

(A) 12

(B) 18

(C) 30

(D) 36

(E) 42

Another way you can do the problem if you just want to think about it is we have two groups of 3 letters that need to be next to each other. This can be arranged into two ways (vowels first or consonants first) then each group has 2 repeats. by looking at the form (ABA) we see there are only 3 positions that B can take.

Now we have 2*3*3 = 18.

Probably best to remember the formulas though.

With
Re: In how many ways can the letters of the word MAXIMA be arran   [#permalink] 22 Aug 2019, 16:53
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