Black and Red vertices of Tree

You are given a tree with $N$ vertices. The vertices are numbered from $1$ to $N$. Some of the vertices are colored black and some are colored red. Also, some vertices can be uncolored. There is at least one black and at least one red vertex. Compute the number of subsets of vertices $W$ such that: - Each vertex in $W$ is uncolored. - $W$ is a connected subgraph of the tree. - If you remove all