Suppose a fair coin is tossed $3$ times. Let the random variable $X$ represent the number of heads on the first and second tosses and let $Y$ represent the number of heads on the second and third tosses. Write the joint probability distribution of $X$ and $Y$.
I solved this problem by making a list, exhaustion, and am wondering if there is an easier way to do this. I can't seem to get it using combinations.