Expected Spanning Trees

You are given a simple undirected graph $G$ with $N$ vertices (numbered $1$ through $N$) and $M$ edges. Consider the following process performed for a fixed number of seconds: - Each second, choose an unordered pair of vertices $(a, b)$ uniformly randomly (there are $N (N - 1) / 2$ such pairs). - If the edge $(a, b)$ is present in the graph, remove it. Otherwise, add it to the graph. We are i