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Combinatorics problem - Please help

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by molins » Tue Nov 24, 2009 3:01 pm
Pls help with this one

In a team of 9 employees, 5 are members of the union. If the team members must form a committee of 4, and if exactly two of the committee members must be members of the union, how many such committees are possible?


OA: 60

Thanks!
Last edited by molins on Fri Nov 27, 2009 5:17 am, edited 1 time in total.
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by mp2437 » Tue Nov 24, 2009 3:15 pm
You have 9 employees, 5 are members, 4 are not. You need to choose a group of 4, and you know that you need exactly 2 employees who are members (out of the 5 possible ones). You have a group of 4, 2 of which are members, that means there are 2 who are non-members.

The only way to get exactly 2 members out of a group of 4 is to have 2 members and 2 nonmembers. You choose them as:

(5C2)*(4C2) = 10 * 6 = 60.
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