Expected Components

You are given a tree with $N$ vertices (i.e, a simple undirected connected graph with $N-1$ edges). $K$ of its vertices are colored black, and the other vertices are white. For every $x$ from $1$ to $K$, solve the following problem: - Find the expected number of connected components in the resulting graph, if you delete *exactly* $x$ randomly chosen black vertices from the tree. Each subset of $x