I need help with this problem. With the remote learning I am having a hard time understanding the problem. Follow the hint if possible. Please explain your reasoning and show all work. Thank you.

-------------

An interplanetary spaceflight map can be represented as a graph G = (V, E), where V is the set of all planetary spaceports and (u, v) E E if there is a spaceflight from u to v. Suppose Pluto simulates a random spaceflight map of the solar system where, for each pair of spaceports, there is a spaceflight available between them (in either direction) with probability p. a. Let random variable F be the total number of spaceflights. Find the expected value of F, justifying your answer. b. Pluto wants to go on a tour of the solar system. Let random variable # be the number of Hamiltonian tours in G. Find the expected value of H, justifying your answer. Note: A tour is defined by the order of the cycle rather than the order from some arbitrary starting vertex. Hence, the tour (a, b, c, a) is the same tour as (b, c, a, b). c. Define the random variable 7 to be the number of triplets of spaceports (a, b, c) such that there is a path of exactly 2 spaceflights from a to c through b. This means that a spaceflight exists from a to b and from b to c, but not from a to c directly. Find the expected value of 7, justifying your answer. Hint: Use indicator random variables