Answer : A committee of 7 has to be formed from 9 boys and 4 girls.
- Exactly 3 girls: If there are exactly 3 girls in the committee, then there must be 4 boys, and the ways in which they can be chosen is
= 504 ways= 4C3 9C4
- At least 3 girls: Here the possibilities are
- 3 girls and 4 boys and
- 4 girls and 3
The number of ways they can be selected
= 588= 4C3X9C4 + 4C4 X9C3
- At most 3 girls:
- 7 boys but no girls
- 6 boys and 1 girl
- 5 boys and 2 girls &
- 4 boys and 3
And the number of their selection is
= 4C3 X9C4 + 4C2 X9C5 + 4C1 X9C6 + 4C0 X9C7
= 1584 ways.