Question

In how many ways a committee of $5$ members to be formed out of $6$boys and $4$ girls if two girls are include in the committee.

Answer 1

Total number of committee which can be formed from $10$ people($6$ boys and $4$ girls) =${}^{10}{C}_5=252$.
When number of girls in a committee is exactly $2$, means no. of boys in committee should be $3$.
So number of combinations having $2$ girls and $3$ boys in committe = ${(}^6{C}_3)\times {(}^4{C}_2)=120$.