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A committee is to be formed comprising 7 members such that there is a simple majority of men and at least 1 woman. The shortlist consists of 9 men and 6 women. In how many ways can this committee be formed?

A committee is to be formed comprising 7 members such that there is a simple majority of men and at least 1 woman. The shortlist consists of 9 men and 6 women. In how many ways can this committee be formed? Correct Answer 4914

Three possibilities: (1W+6M), (2W+5M), (3W+4M)= (6C1 × 9C6) + (6C2 × 9C5) + (6C3 × 9C4)
= 4914

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