Given, A committee of 7 has to be formed from 9 boys and 4 girls. A committee of at most 3 girls consists of (1) No girl, 7 boys (2) 1 girl, 6 boys (3) 2 girls, 5 boys (4) 3 girls, 4 boys Total number of ways that consists of at most 3 girls =(4C0)(9C7)+(4C1)(9C6)+(4C2)(9C5)+(4C3)(9C4) =(
4!
0!(4)!
)(
9!
2!(7)!
)+(
4!
3!(4)!
)(
9!
3!(6)!
)+(
4!
2!(2)!
)(
9!
4!5!
)+(
4!
1!(3)!
)(
9!
5!4!
). =36+336+756+504 =1632 Hence, A committee of 7 has to be formed from 9 boys and 4 girls. total number of ways can this be done when the committee consists of at most 3 girls is 1632.