Algorithm analysis class

Problem 5. Given a graph G (V, E) and two vertices u, v V, a simple path from u to v in G is a sequence of k + 1 distinct vertices p-vo, ui, , th such that to u, tk = t, and (ti-i, ti) e E for 1 SiS 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 specific number of distinct simple paths between a pair of vertices in Ke