Question: 1. Show that for a fixed r ∈ N and any n ∈ N,
2. A bridge is an edge of a graph G whose removal disconnects the graph. Prove that an edge e is a bridge if and only if it is contained in every spanning tree of G.
3. A computer science department has eight faculty members, three of whom have the last name Jeong. How many ways can two representatives to the Faculty Council be chosen so that one representative has the last name Jeong and the other does not?