Question

If exactly 4 boys volunteer, what is the probability that the team is all boys or no boys?

Answer 1

There is not enough information to make conclusions. We assume in addition that there are 4 boys, m girls and the aim is to make a team with n persons, $n\leq m+4$ . In case we want to make a team from 4 boys, the total number of choices is: $C_{n-4}^{m}=\frac{(n-4)!}{m!(n-4-m)!}$ . I.e., we take 4 boys and for the other places take m girls. In case we wish to make a team with no boys, the number of choices is: $C_n^m=\frac{n!}{(n-m)!m!}$.