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# 4 women and 6 men work in the accounting department. In how

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Manager
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4 women and 6 men work in the accounting department. In how [#permalink]

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08 Jul 2008, 07:25
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4 women and 6 men work in the accounting department. In how many ways can a committee of 3 be formed if it has to include only one woman?

Director
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08 Jul 2008, 07:32
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Committee of 3 will include 1 woman and 2 men as per the question.

Total Women = 4
Number of ways to select 1 woman out of 4 = 4C1 = 4

Total Men = 6
Number of ways to select 2 men out of 6 = 6C2 = 15

Total number of ways = 4 * 15 = 60
Intern
Joined: 01 Jul 2008
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08 Jul 2008, 07:38
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just wanted a confirmation

the reason to multiply 4 with 15 is "select 1 woman AND 2 men" => 4*15
Director
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08 Jul 2008, 07:37
excellent solution!
Manager
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08 Jul 2008, 07:41
Thanks ahijit. I appreciate it. +1
Thanks parag.
Director
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08 Jul 2008, 07:55
# of ways 1 woman can be selected out of 4* # of ways 2 men can be selected out of 6= 4C1 * 6C2 = 4 * 15 = 60
Director
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08 Jul 2008, 08:22
hi0parag wrote:
just wanted a confirmation

the reason to multiply 4 with 15 is "select 1 woman AND 2 men" => 4*15

Yes you are absolutely correct.
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08 Jul 2008, 09:02
stingraybullray wrote:
4 women and 6 men work in the accounting department. In how many ways can a committee of 3 be formed if it has to include only one woman?

WMM = 4 * 6C2 = 4*15 =60
Re: Combinatorics - Committee   [#permalink] 08 Jul 2008, 09:02
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