2017 AIME II Problems/Problem 11

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$\textbf{Problem 11}$ Five towns are connected by a system of raods. There is exactly one road connecting each pair of towns. Find the number of ways there are to make all the roads one-way in such a way that it is still possible to get from any town to any other town using the roads (possibly passing through other towns on the way).

$\textbf{Problem 11 Solution}$ $\boxed{544}$