Question
Determine the total number of ways to form a committee
consisting of 10 members from a pool of 8 men and 7 women, ensuring the committee includes at least 6 men and at least 3 women.Solution
Number of ways of selecting a committee with 6 men and (10 - 6) women =Â 8C6Â XÂ 7C4 = 28 X 35 = 980 Number of ways of selecting a committee with 7 men and 3 women =Â 8C7Â XÂ 7C3 = 8 X 35 = 280 So, total number of ways of forming a committee under the given conditions = 980 + 280 = 1260
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