In how many ways this can be done if atleast 5 women have to be included in a committee?

6000

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6010

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6062

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6005

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None of these

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Solution

The correct option is C 6062
There are 9 women and 8 men. A committee of 12, consisting of atleast 5 women, can be formed by choosing
(i) 5 women and 7 men
(ii) 6 women and 6 men
(iii) 7 women and 5 men
(iv) 8 women and 4 men
(v) 9 women and 3 men
$∴$ Total number of ways of forming the committee
$=^{9} C_{5} \times^{8} C_{7} +^{9} C_{6} \times^{8} C_{6} +^{9} C_{7} \times^{8} C_{5} +^{9} C_{8} \times^{8} C_{4} +^{9} C_{9} \times^{8} C_{3} = 126 \times 8 + 84 \times 28 + 36 \times 56 + 9 \times 70 + 1 \times 56$
= 1008+ 2352 + 2016 + 630 + 56 = 6062

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