SOLUTION: A committee is to be formed comprising of 7 member such that there is a majority of men and at least 1 woman in every committee.The shortlist consists of 9 men and 6 women.In how m
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Question 1135741: A committee is to be formed comprising of 7 member such that there is a majority of men and at least 1 woman in every committee.The shortlist consists of 9 men and 6 women.In how many ways can this be done?
You can put this solution on YOUR website! The problem states that the committee must have a majority of men AND have at least one woman. That means the committee must be comprised of six men and one woman, five men and two women, or four men and three women.
Ways a committee with 6 men and 1 woman could be formed:
9C6 * 6C1 = 84 * 6 = 504
Ways a committee with 5 men and 2 women could be formed:
9C5 * 6C2 = 126 * 15 = 1890
Ways a committee with 4 men and 3 women could be formed:
9C4 * 6C3 = 126 * 20 = 2520
Add all these together: 504 + 1890 + 2520 = 4914.
So, there are 4914 different possible combinations.
