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Question
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: exactly 3 girls?
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Solution
A committee of 7 members is to be formed from 9 boys and 4 girls.
When there are 3 girls in that committee, then there will be 4 boys in that committee. Ways to choose 3 girls and 4 boys
= 4C3 x 9C4
= 4C1 x 9C4
[∵ 4C3 = 4C1]
= `4/1 xx (9 xx 8 xx 7 xx 6)/(1.2.3.4)`
= 9 x 8 x 7 = 504
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