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?

4914

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3630

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3724

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3824

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Solution

The correct option is A $4914$
Members for forming committee $= 7$
Men strength $= 9$
Women strength $= 6$
The possible cases considering he above conditions forms the ordered pairs of (Men, Women) as $(6, 1), (5, 2), (4, 3)$ .
The possible groups will be $^{9} C_{6} .^{6} C_{1} +^{9} C_{5} .^{6} C_{2} +^{9} C_{4} .^{6} C_{3} = 504 + 1890 + 2520 = 4914$
Hence the correct answer is $4914$

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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?