Give a combinatorial proof that if n is a positive integer then ∑n k =0 k2 (n k ) = n(n + 1)2n−2.[Hint: Show that both sides count the ways to select a subset of a set of n elements together with two not necessarily distinct elements from this subset. Furthermore, express the righthand side as n(n − 1)2n−2 + n2n−1.]