Question

There are 6 boys and 3 girls in a class. An entertainment committee of 5 is to be selected such that their are 3 boys and 2 girls in a committee. In how many ways can the committee be selected? What are the number of ways if their is at least one girl?

Answer 1

3 boys are selected fry 6boys and 2girls selected from 3girls in

6C3×3C2

=6!/3!(6-3)!×3!/2!×(3-2)!=(6×5×4×3!/3!×3!)×(3×2!/2!×1!)

20×3=60 ways

The required ways if there is at least one girl is 2^3-1=8-1=7ways