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In how many ways can you arrange the letters "APTITUDE" so

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In how many ways can you arrange the letters "APTITUDE" so [#permalink]

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In how many ways can you arrange the letters "APTITUDE" so as to form words that begin and end with a vowel?

A. 640
B. 1280
C. 4320
D. 8640
E. 9860
[Reveal] Spoiler: OA

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Re: Aptitude [#permalink]

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New post 02 Dec 2009, 00:52
APTITUDE has 8 letters, so given that the letters start and end with a vowel there are 2 conditions.

1) There are 4 choose 2 possibilities for a vowel start/end combination. [Any 2 out of A,I,U,E]

2) The remaining 6 letters can be arranged in any order and still form a word. Thus permutate 6 objects.

Answer = (4!/2!2!)*6!= 4320

Edit : Given T is repeated and non vowel. I think the final answer should be divided by 2! to give 2160 (which is not an option)

Would love to get some advise!

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In how many ways can you arrange the letters "APTITUDE" so [#permalink]

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New post 02 Dec 2009, 01:33
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prome2 wrote:
APTITUDE has 8 letters, so given that the letters start and end with a vowel there are 2 conditions.

1) There are 4 choose 2 possibilities for a vowel start/end combination. [Any 2 out of A,I,U,E]

2) The remaining 6 letters can be arranged in any order and still form a word. Thus permutate 6 objects.

Answer = (4!/2!2!)*6!= 4320

Edit : Given T is repeated and non vowel. I think the final answer should be divided by 2! to give 2160 (which is not an option)

Would love to get some advise!


We have 4 vowels, as order matters in this case # of arrangements of 4 vowels in 2 slots (begin/end) will be 4P2=12

Now we are left with 8-2=6 letters, from which 2 letters are the same (T). # of arrangements 6!/2!=360

Total=360*12=4320

Answer: C.

So I think the answer is right.You just didn't consider that order matters in the first case and repeated T in the second case, but these two mistakes compensated each other and you got the correct answer.

Hope it's clear.
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Re: Aptitude [#permalink]

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New post 02 Dec 2009, 04:31
Crystal! Thanks Bunuel! +1

Last edited by prome2 on 02 Dec 2009, 20:09, edited 1 time in total.

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Re: In how many ways can you arrange the letters "APTITUDE" so [#permalink]

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Re: In how many ways can you arrange the letters "APTITUDE" so   [#permalink] 16 Sep 2017, 22:11
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