Question

If a five-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of dealing two pairs?(two cards of one rank, two cards of a second rank, and one card of a third rank)

Answer 1

198/4165

Answer 2

\[\frac{\left(\begin{matrix}13 \\ 3\end{matrix}\right)\left(\begin{matrix}3 \\ 1\end{matrix}\right)\left(\begin{matrix}4 \\2\end{matrix}\right)^2\left(\begin{matrix}4 \\ 1\end{matrix}\right)}{\left(\begin{matrix}52 \\ 5\end{matrix}\right)}\]