Question: Assume you have a deck with with $52$ cards ($4$ suites of $13$ cards: numbers $1\ldots 9$, and faces J,Q,K). What is the probability you draw jack of hearts in a hand of $5$?
My way of thinking is the following:
$\frac{\left(\dfrac{1\cdot51\cdot50\cdot49\cdot48}{4!}\right)}{ \left(\dfrac{52\cdot51\cdot50\cdot49\cdot48}{5!}\right)}$
$1$ is for the jack of hearts being drawn, and then $51\ldots48$ for the rest of the $4$ cards