5) Starting with no edges between A and B, if |E| many edges are added between A and B uniformly at random, what is the expected number of perfect matchings in the resulting graph? Hint: if S is a set of edges in a potential perfect matching, let Xs = 1 if all the edges in S are added to the graph, and Xs = 0 if any of them are missing. What is E[Xs]?

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