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:
(i) exactly 3 girls?
(ii) at least 3 girls?
(iii) at most 3 girls?
(i) exactly 3 girls
This means you have to choose 3 girls from 4 and 4 boys from 9 to form a committee of 7. This can be done in
4C3×9C4
(ii) At least 3 girls
This means girls can either be 3 or 4
So first choose 3 girls and 4 boys or 4 girls and 3 boys
Total ways = 4C3×9C4 + 4C4×9C3
(iii) At most 3 girls
This means we have to choose 1 or 2 or 3 girls
So this can be done in
4C0×9C7+4C1×9C6 + 4C2×9C5 + 4C3×9C4 ways.