A committee of 5 members is to be formed from 6 men and 4 women. In how many ways can the committee be formed if it must contain exactly 3 men and 2 women?

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Accepted Answer

120. Choose 3 men from 6 in C(6,3) = 20 ways and 2 women from 4 in C(4,2) = 6 ways. Total = 20 x 6 = 120. (252 = C(10,5) ignores the required composition; 720 uses P(6,3) instead of C(6,3) — order does not matter inside a committee.)

A committee of 5 members is to be formed from 6 men and 4 women. In how many ways can the committee be formed if it must contain exactly 3 men and 2 women?

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