Hello,

$G(n,m)$ is the family of all graphs with $n$ vertices and $m$ edges (I consider $m < n$).
Each graph in $G(n,m)$ is selected with uniform probability.
What is the probability that the graph selected has exactly $c$ connected components?

An equivalent question is: what is the probability that exactly $k$ edges should be removed from the selected graph in order to make it a forest (graph without cycles)?

There is a solution for the case of $k = 0$ <a href="https://mathoverflow.net/questions/57062/probability-that-a-graph-g-does-not-contain-a-cycle">here</a>.

Thank you.