Overcard Probability

[Paxosmotic]

This is a problem me and another 2+2er have been trying to figure out for a few weeks (off an on, obviously, I like sleep), but haven't pieced together. I know the chance of at least one overcard on a flop is represented by p=1-(50-n choose 3)/(50 choose 3) where n is number of overcards, but what we are trying to figure out is the probability of exactly 1 overcard to 99, exactly 2 overcards to 77, and so forth. How would one represent an equation to find the chance of 0, 1, 2, or 3 overcards to a given pocket pair, from 3 overcards to AA being 0% and 1 overcards to 22 being 100% and everything inbetween? Anyone have any ideas?