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Quantitative Aptitude

Derangement

In how many o...

Question

In how many of these committees the women are in majority?

A

2000

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B

2700

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C

2705

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D

2702

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E

None of these

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Solution

The correct option is D 2702
Women are in majority in (iii), (iv) and (v) cases.
$∴$ Total number of such committees
$=^{9} C_{7} \times^{8} C_{5} +^{9} C_{8} \times^{8} C_{4} +^{9} C_{9} \times^{8} C_{3} = 36 \times 56 + 9 \times 70 + 1 \times 56$
= 2016 + 630 + 56
= 2702

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