SOLUTION: A committee of 6 persons to be formed from 4 men and 6 women.In how many ways can this be done when atmost 3 women are included?
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Question 1086412: A committee of 6 persons to be formed from 4 men and 6 women.In how many ways can this be done when atmost 3 women are included? Answer by math_helper(2461) (Show Source):
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1. If the committee has exactly 3 women:
#ways of selecting 3 women * # ways of selecting 6-3=3 men:
(6C3) x (4C3) = 6!/(3!*3!) * 4!/(3!*1!) = 20 * 4 = 80 ways
2. If the committee has exactly 2 women:
(6C2) x (4C4) = 6!/(4!*2!) * 4!/(4!0!) = 15 * 1 = 15 ways
Those are the only two possibilities for #women and #men because if you tried to form the committee with just 1 woman, there wouldn't be enough men to make a committee of 6.
Thus, the answer is 80+15 = ways
