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\begin{enumerate}

\item[A]
{\bf Derangements:} $n$ people leave their hats in the coatroom. On the
way out the person in charge of the coatroom hands their hats back to
them in an arbitrary order. Use inclusion-exclusion to count the total
number of ways the hats can be handed back to them so that no person
gets their own hat back.

\item[B]
Use generating functions to compute ${\sum_{i=0}^n i(i-1)(i-2)}$.

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