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The board of a small nonprofit has nine members: three men and six women.

Mathematics
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The board of a small nonprofit has nine members: three men and six women.  If they want to form a committee of three people to study a proposed course of action, in how many different ways could they choose the members of the committee?

In the scenario from question 1, how many ways could they choose a committee if there needs to be at least one man and at least one woman on the committee?

Apr 12th, 2015

1) A 3 member comittee put of 9  members can be formed by 9 C 3 ways.

9C3 = 9!/ 3! (9 - 3)! = 84

2) One man can be chosen in 3 ways , one women in 6 ways....

3 rd member can be chosen in 7 ways as two people already selected out of 9 ,

Hence, 3 x 6 x 7 = 126 




Apr 12th, 2015

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