Question

A committee of $7$ has to be informed from $9$ boys and $4$ girls. In how many ways can this done when the committee consists of:
(i) exactly $3$ girls (ii) atleast $3$ girls (iii) atmost $3$ girls

Answer 1

No. of goals in committee - No of ways

$0$ ${}^9{C}_7.{}^4{C}_0$

$1$ ${}^9{C}_6.{}^4{C}_1$

$2$ ${}^9{C}_5.{}^4{C}_2$

$3$ ${}^9{C}_4.{}^4{C}_3$

$4$ ${}^9{C}_3.{}^4{C}_4$

(i) ${}^9{C}_4.{}^4{C}_3$

(ii) ${}^9{C}_4.{}^4{C}_3+{}^9{C}_3.{}^4{C}_4$

(iv) ${}^9{C}_7.{}^4{C}_0+{}^9{C}_6.{}^4{C}_1+{}^9{C}_5.{}^4{C}_2+{}^9{C}_4.{}^4{C}_3$