Question

A committee of 7 has to be formed 9 boys and 4 girls in how many ways can this be done when the committee consist of exactly 3 girls?

Answer 1

Number of girls $=4$

Number of boys $=9$

Since the committee has to consists exactly $3$ girls, the committee can consist of $3$ girls and $4$ boys.

$\therefore 3$ girls out $4$ can be selected in ${}^4{C}_3$ ways out of $4$ boys out of $9$ can be selected in ${}^9{C}_4$ ways.

$\therefore$ required number of ways ${=}^4{C}_3{\times }^9{C}_4$

$=4\times \frac{9\times 8\times 7\times 6}{4\times 3\times 2\times 1}=504$