Question
A team of 6 players is to be selected from 7 men and 5
women. In how many ways can a team be formed such that at least 4 men are included?Solution
We consider possible cases where the number of men is at least 4.
Case I: 4 men and 2 women:
7 C 4 × 5 C 2 = 35 × 10 = 350
Case II: 5 men and 1 woman:
7 C 5 × 5 C 1 = 21 × 5 = 105
Case III: 6 men and 0 women:
7 C 6 × 5 C 0 = 7 × 1 = 7
Total = 350 + 105 + 7 = 462 ways
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