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# ON how many ways can the letters of the word

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Manager
Joined: 23 Mar 2008
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ON how many ways can the letters of the word [#permalink]  17 Aug 2008, 01:52
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ON how many ways can the letters of the word "COMPUTER" be arranged if vowels occupy the even positions?
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Kudos [?]: 2140 [0], given: 359

Re: PS: combinatorics [#permalink]  17 Aug 2008, 02:40
Expert's post
vowels - o,u,e (no repetitions)
consonants - c,m,p,t,r (no repetitions)

patterns: cvcvcvcc, cccvcvcv, cvcccvcv, cvcvcccv - four possibilities ($$C_3^4$$)

the total number: $$N=C_3^4*P_3^3*P_5^5=4*6*120=2880$$
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Manager
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Re: PS: combinatorics [#permalink]  17 Aug 2008, 03:16
Alr8 here's my way

There are 4 even positions; the three vowels (O, E, U) can select 3 out of 4 of these positions in 4C3 ways. The three vowels thn can arrange themselves in 3! ways. The rest of the 5 consonants can occupy the rest of the five position in 5C5 ways and arrange themselves in 5C5*5! ways.
Total no. of ways = 4c3*3!*5c5*5! = 4*6*120 = 2880
Re: PS: combinatorics   [#permalink] 17 Aug 2008, 03:16
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