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Quantitative Aptitude

Combination

A committee i...

Question

A committee is to be formed comprising of 6 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?

4721

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4921

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2646

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Solution

The correct option is C
2646

The number of ways in which a committee can be formed having at least one woman is = $^{9} C_{5}$ $\times$ $^{6} C_{1}$ + $^{9} C_{4}$ $\times$ $^{6} C_{2}$ = 2646

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A committee is to be formed comprising of 6 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?

The correct option is C 2646 The number of ways in which a committee can be formed having at least one woman is = 9C5 × 6C1 + 9C4 × 6C2 = 2646

The correct option is C
2646

The number of ways in which a committee can be formed having at least one woman is = $^{9} C_{5}$ $\times$ $^{6} C_{1}$ + $^{9} C_{4}$ $\times$ $^{6} C_{2}$ = 2646