\problemdata
{s01-ps7}
{bug}
{counting}

\begin{problem} Solve the following counting problems. Give your answers in terms of factorials and binomial coefficients and then evaluate them.
\begin{problemparts}

\problempart A bug starts at position $(0, 0)$ and wants to reach
position $(4, 6)$ in 10 steps.  Each step is either north, south,
east, or west; that is, each step either increments or decrements one
coordinate.  How many different paths can the bug choose from?

\problempart How many five-card poker hands contain no diamonds?

\problempart A flush in poker is a hand with all cards from the same
suit.  How many flushes are there?

\problempart A straight in poker is a hand with 5 consecutive card
values (no wraparound, and suite don't matter).  How many straights
are there?

\problempart How many straight flushes are there?

\end{problemparts}  
\end{problem}