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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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Location: SF Bay Area, USA
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In how many ways can the laetters of the word "COMPUTER" be [#permalink]  05 Jan 2005, 22:36
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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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
Joined: 06 Sep 2004
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(1) 8!
(2) 7!
(3) 6! X 3!
(4) 8! - 6! X 3!
(5) 4! X 5!
Director
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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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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.
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# In how many ways can the laetters of the word "COMPUTER" be

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