\problemdata
{s01-ps10}
{random variable}

\begin{problem}
There are $n$ MIT students who are taking 6.042 and 6.003 this term.  To
make it easier on themselves, the professors in charge of these classes
have decided to randomly permute their class lists and then assign
students grades based on their rank in the permutation\footnote{\dots just
as many students have suspected \texttt{:-)}}.  Assume all permutations
are equally likely and that the ranking in each class is independent of
the other.

\begin{problemparts}

\problempart
What is the expected number of students that have a higher rank
in 6.042 than 6.003?

\problempart
What is the expected number of students that have a ranking at
least $k$ higher in 6.042 than in 6.003?

\end{problemparts}
\end{problem}
