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\begin{itemize}
\item No of different shortest paths from $(0,0)$ to $(m,n)$ and
  binomial coefficients.
\item Number of terminal zeros in $100!$.
\item Number of ways for occupants to leave $n$ houses in a row so
  that for all but the last a neighbor can check on the house once the
  occupant has left.
\item Number of surjective functions.
\item Number of derangements.
\item 

\end{itemize}

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