Question

Find the number of ways of forming a committee of $5$ members from $6$ men and $3$ women.

Answer 1

A committee of $5$ members can be formed from $6$ men and $3$ women in four ways

Committee with $5$ men and $0$ women can be formed in ${}^6{C}_5\times {}^3{C}_0=6\times 1=6$ ways

Committee with $4$ men and $1$ women can be formed in ${}^6{C}_4\times {}^3{C}_1=15\times 3=45$ ways

Committee with $3$ men and $2$ women can be formed in ${}^6{C}_3\times {}^3{C}_2=20\times 3=60$ ways

Committee with $2$ men and $3$ women can be formed in ${}^6{C}_2\times {}^3{C}_3=15\times 1=15$ ways

Total number of ways will be $6+45+60+15=126$ ways