\instatements{\newpage}

\begin{examproblem}{20}
Each card in a 52-card deck has a suit ($\spadesuit, \heartsuit,
\clubsuit, \diamondsuit$) and a value ($A, 2, 3, \ldots, 9, 10, J, Q,
K$).  For this problem, the value of an ace ($A$) is below the value
of a 2.

\bparts

\ppart[5] How many different five-card hands contain no two cards with
the same value?  For example, $5 \heartsuit\ 4 \clubsuit\ Q\
\spadesuit\ K\ \spadesuit\ 10 \heartsuit$ is such a hand, but $8
\clubsuit\ 8 \diamondsuit\ J \clubsuit\ Q \heartsuit\ 7 \clubsuit$ is
not.

\solution[\vspace{1.5in}]{
\[
\binom{13}{5} \cdot 4^5
\]
}

\ppart[7] How many different five-card hands contain no two cards with
the same or consecutive values?  For example, $A \heartsuit\ 4
\clubsuit\ J \heartsuit\ K \diamondsuit\ 7 \diamondsuit$ is such a
hand, but $5 \heartsuit\ 4 \clubsuit\ Q\ \spadesuit\ K\ \spadesuit\ 10
\heartsuit$ is not.

\solution[\vspace{1.5in}]{
\[
\binom{9}{5} \cdot 4^5
\]
}

\ppart[8] How many hands contain 

\solution{
Several types of hand satisfy this condition:
\[

\]
}

\eparts

\end{examproblem}