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Quantitative Aptitude

Combination

A group has t...

Question

A group has to be formed comprising 8 members such that there is a simple majority of men and atleast one woman. There are 8 men and 7 women. In how many ways it can be done?

A

2584

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B

2604

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C

2684

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D

2704

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Solution

The correct option is B 2604
Three possibilities
1W + 7 M, 2W + 6 M and 3 W + 5 M
$= (^{7} C_{1} \times^{8} C_{7}) + (^{7} C_{2} \times^{8} C_{6}) + (^{7} C_{3} \times^{8} C_{5}) = 56 + 588 + 1960 = 2604$

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