Editorial for Another Contest 7 Problem 4 - Team Assignments

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The graph structure does not matter - there are $K(K-1)^{N-1}$ ~K(K-1)^{N-1}~ ways to $K$ ~K~-color a tree with $N$ ~N~ vertices.

To count the number of such colorings that use all $K$ ~K~ colors, use inclusion-exclusion.

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