A five card hand is dealt from a standard 52-card deck. What is the probability that there will be exactly three suits in the hand?
The Attempt at a Solution
I started with (4 C 3)(39 C 5), but this gives me all possible hands with three or less suits. How do I get rid of the the possibility of 2 or 1 suits? I tried (4 C 3)(39 C 5) - (4 C 2)(26 C5), but I am not certain that gets rid of all possible overlaps between the sets.