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# In how many ways can the laetters of the word "COMPUTER" be

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Director
Joined: 19 Nov 2004
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In how many ways can the laetters of the word "COMPUTER" be [#permalink]

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05 Jan 2005, 23:36
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

In how many ways can the laetters of the word "COMPUTER" be arranged
1) Without any restriction
2) M must always occur at the third place
3) All the vowels are together
4) All the vowels are never together
5) Vowels occupy the even positions

CIO
Joined: 09 Mar 2003
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06 Jan 2005, 02:29
I would worry only about the first two for the gmat. The rest aren't important.

The first one is 8!.

In the second one, we're placing the M at the third spot, so that leaves only 7 options for the first spot, 6 for the second, 5 for the 4th, and so on. It looks like:

7x6x1x5x4x3x2x1 (which is 7!)

Note that the last one is impossible, as there are 4 even spots, but only three vowels.
Manager
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06 Jan 2005, 05:54
(1) 8!
(2) 7!
(3) 6! X 3!
(4) 8! - 6! X 3!
(5) 4! X 5!
Director
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06 Jan 2005, 10:44
I got the same answers as ssumitsh. Thanks for confirming.

Ian, I guess the question means that the O, U, E must all have to be in either of 2, 4, 6, 8 postions. 3 vowels will occupy the 3 even positions and a consonant will occupy the other even postion.
CIO
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06 Jan 2005, 10:50
nocilis wrote:
I got the same answers as ssumitsh. Thanks for confirming.

Ian, I guess the question means that the O, U, E must all have to be in either of 2, 4, 6, 8 postions. 3 vowels will occupy the 3 even positions and a consonant will occupy the other even postion.

yeah, i thought about that later. I just don't think it's really an issue. I've never seen anything even that challanging on the GMAT, nor have I heard of anyone seeing anything like that.

I really try not to overstress about combinations. There are so many other more important topics to learn the nuances of. This one's usually right there on the surface.
06 Jan 2005, 10:50
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