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{\bf Worksheet \#15; date: 10/17/2018}
{\bf MATH 55 Discrete Mathematics}
\begin{enumerate}
\item A coin is fliped $10$ times where each flip comes up either heads or tails. How many possible outcomes contains more heads than tails?
\item How many ways are there to seat $12$ people around a circular table? What if they are $3$ couples who all want to sit next to their spouses?
\item {\em (Rosen 6.4.9)} What is the coefficient of $x^{101} y^{99}$ in the expansion of $(2x - 3y)^{200}$?
\item {\em (Rosen 6.4.25; modified)} Let $n$ be a positive integer. Show that
\[
2 \binom{2n}{n+1} + 2 \binom{2n}{n} = \binom{2n+2}{n+1}.
\]
\item Show the identity above with a combinatorial argument.
\end{enumerate}
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