\documentstyle[12pt]{article}
\include{macros-course}

\begin{document}

\begin{problems}

\problem 
In how many ways can the letters in the English alphabet be arranged
so that there are exactly seven letters
between the letters $a$ and $b$?
(With {\em arrangment} of letters we mean a sequence 
that contains each letter exactly once.)


\problem 
Use a combinatorial argument to show that
\[C(2n,2) = 2 C(n,2) + n^2\]


\end{problems}


\end{document}

