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

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Manager
Joined: 22 Jul 2008
Posts: 81
Location: Bangalore,Karnataka
In how many ways can you arrange the letters "APTITUDE" so  [#permalink]

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02 Dec 2009, 00:24
1
2
00:00

Difficulty:

65% (hard)

Question Stats:

58% (01:39) correct 42% (01:57) wrong based on 118 sessions

### HideShow timer Statistics

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

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Intern
Joined: 25 Nov 2009
Posts: 30

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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.

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!
Math Expert
Joined: 02 Sep 2009
Posts: 51121
In how many ways can you arrange the letters "APTITUDE" so  [#permalink]

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02 Dec 2009, 01:33
3
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.

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

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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Intern
Joined: 25 Nov 2009
Posts: 30

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Updated on: 02 Dec 2009, 20:09
Crystal! Thanks Bunuel! +1

Originally posted by prome2 on 02 Dec 2009, 04:31.
Last edited by prome2 on 02 Dec 2009, 20:09, edited 1 time in total.
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Joined: 09 Sep 2013
Posts: 9128
Re: In how many ways can you arrange the letters "APTITUDE" so  [#permalink]

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02 Dec 2018, 18:43
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Re: In how many ways can you arrange the letters "APTITUDE" so &nbs [#permalink] 02 Dec 2018, 18:43
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