Let Kn be the complete graph on n vertices and 3 <= r <= n. How many subgraphs isomorphic to Pr and subgraphs isomorphic to Cr does Kn have? Note: Pr is the path graph with the set of vertices {v1, v2, ..., vr} and the set of edges {v1v2, v2v3, ..., vr-1vr} and Cr is the cycle graph with the set of vertices {v1, v2, ..., vr} and the set of edges {v1v2, v2v3, ..., vr-1vr, vrv1}. The answers would be 17, 7, 3, 1 for r = n = 3 and 112, 15, 12, 4 for r = 3, n = 4.