From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
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the committee of 5 persons can be chosen as:
1. 3 men and 2 women = 7C3 * 6C2 = 4*5*6*7*5*6 = 25200
2. 4 men and 1 women = 7C4 * 6C1 = 5*6*7*6 = 1260
3. 5 men and no women = 7C5 * 6C0 = 6*7*1 = 42
total ways = 25200 + 1260 + 42 = 26502
1. 3 men and 2 women = 7C3 * 6C2 = 4*5*6*7*5*6 = 25200
2. 4 men and 1 women = 7C4 * 6C1 = 5*6*7*6 = 1260
3. 5 men and no women = 7C5 * 6C0 = 6*7*1 = 42
total ways = 25200 + 1260 + 42 = 26502
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