Question

A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them, if there have to be 3 exactly girls in the invitees?

Answer 1

Choosing 3 girls from 5 girls is equal to 5 C 3 { Choose 3 from 5 = 5!(5−2)!.2! = 5!3!.2! = 10}

Now since 0,1,2,3 or 4 out of 4 boys can be invited you have to sum over 4 C 0 + 4 C 1+ 4 C 2 + 4 C 3 + 4 C 4 = 24 = 16 ways.

The number of possible ways would be inviting the girls x boys = 10 x 16 = 160

I hope this will help you