[10 pts] Suppose John's biking environment consists of n ≥ 3 landmarks, which are linked

by bike route in a cyclical manner. That is, there is a bike route between landmark 1 and 2,

between landmark 2 and 3, and so on until we link landmark n back to landmark 1. In the

center of these is a mountain which has a bike route to every single landmark. Besides these,

there are no other bike routes in the biking environment.

You can think of the landmarks and the single mountain as nodes, and the bike routes as edges,

which altogether form a graph G. A path is a sequence of bike routes.

(a) [6 pts] Find the number of paths of length 2 in the graph in terms of n. Justify your

answer.

(b) [6 pts] Find the number of cycles of length 3 in the graph in terms of n. Justify your

answer.

(c) [6 pts] Find the number of cycles in the graph in terms of n. Justify your answer.