Problem 5. Given a graph G = (V;E) and two vertices u; v 2 V , a simple path from u to v in G is a sequence of k + 1 distinct vertices p = v0; v1; : : : ; vk such that v0 = u; vk = v, and (vi1; vi) 2 E for 1 i k. Furthermore, the complete graph with n vertices, denoted by Kn, is an undirected graph with n vertices such that there is an edge between any pair of vertices. Derive a formula for the number of distinct simple paths between a given pair of distinct vertices u; v in Kn, for any n. Give the speci c number of distinct simple paths between a pair of vertices in K6.