Show that, with n relations, there are (2(n − 1))! / (n−1)! Different join orders. If you wish, you can derive the formula for the number of complete binary trees with n nodes from the formula for the number of binary trees with n nodes. The number of binary trees with n nodes is 1/n+1 (2n n); this number is known as the Catalan number, and its derivation can be found in any standard textbook on data structures or algorithms.