A boy is selected at random from amongst the children belonging to families with n children. It is known that he has at least two sisters. Show that the probability that he has k − 1 brothers is
\frac { (n-1)! }{ ({ 2 }^{ n-1 }-n)(k-1)!(n-k)! },
for 1 ≤ k ≤ n − 2 and zero for other values of k. Assume that boys and girls are equally likely.