\problemdata
{s01 ps10}
{random variable}
{linearity}

\begin{problem} There is a dinner party for $n \geq 2$
couples.  The hostess chooses a seating arrangement for the $2n$
people around a circular table uniformly at random.  What is the
expected number of couples such that the husband and wife are sitting
next to each other?

\hint Use indicator random variables and linearity of expectation. What's the probability that Mr. Jones is sitting next to Mrs. Jones? 

\end{problem}