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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: at least 3 girls?
Solution
If there are at least 3 girls in the committee then the committees will be formed as follows:
- 3 girls, 4 boys
- 4 girls, 3 boys
Total ways of forming these committees = 4C3 x 9C4 + 4C4 x 9C3
= 4C1 x 9C4 + 1 x 9C3
= `4 xx (9 xx 8 xx 7 xx 6)/(1 xx 2 xx 3 xx 4) + (9 xx 8 xx 7)/(1 xx 2 xx 3)`
= 504 + 84
= 588
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