I'd like to think I know a little about math and some basic probability based on the class I took in college, but then again maybe I don't. lol Anyway, I have no idea how to figure the probability on this. Anyone care to take a crack at it for fun?

In Div 1 college football there are 119 teams. In the last 2 years 3 former asst coaches from the same University who became head coaches at other schools were fired due to misconduct/mistreatment of players. What are the chances, based on random chance alone, that all 3 coaches were hired from the same school?

Obviously, many head coaches were asst at multiple schools before becoming head coaches. But, usually (as is the case here) they spent the majority of time at one school and are known primarily for that school they were hired from. Let's assume for the sake of this problem that there is only one school they are associated with as an asst coach. I'm trying to make this as simple as possible.

Unfortunately, I'm not exactly sure how many TOTAL coaches were fired for misconduct with players during that time span. So, I'd like to get the probability for four different possibilities (it is almost certainly one of these four), 3 total, 4 total, 5 total, and 6 total. Obviously, if I had the formula I could just insert the four different numbers to get the answer.

Any idea what the formula would be?