From a bridge deck of $52$ cards, we draw $13$. What is the probability that we have $5$ spades in our hand?
I think that there are $\dfrac{52!}{13! \cdot 39!}$ ways we can choose $13$ cards. There are $\dfrac{13!}{5! \cdot 8!}$ ways to have $5$ spades in our hand.
$P = \frac{\left(\dfrac{13!}{5! \cdot 8!}\right)}{\left(\dfrac{52!}{13! \cdot 39!}\right)}.$
Am I doing something wrong?