A five-card poker hand may contain from zero to four aces. If $X$ is the random variable denoting the number of aces, enumerate the range space of $X$. What are the probabilities associated with each possible value of $X$?
Edit: enumerates the range space just means the set range for random variable $X$; this set is $\{0,1,2,3,4\}$. My problem is with probability calculus. As I know, $P_X(1)$, for example, should be equal to probability to have one ace, something like $k$ combinations of $s$, with $k= 4$, $s=$(# total hands $-1$), this divided by total hands combinations, but the results are not equal to book answer, so i guess my probability calculus is wrong.
I already managed to find the answer, the probability $P_x(X=k)$$=\frac{{4\choose{k}}{48\choose{5-k}}}{52\choose5}$. My confusion was given by a typo in the answer of the book.