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\item[A]
{\bf The Catalan number problem.}  $2n$ people stand in line to buy a
cinema ticket which costs $50$ cents. Half the people each have $1$
dollar and the other half each have $50$ cents. In how many ways can
they stand in line so that the person in the ticket booth always has
change (if needed) for the person in front of the window?

\item[B]
How many different paths of length $N$ are there from $(0,0)$ to $(p,q)$? 

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