I've been playing a game recently where two teams of 5 random characters from a pool of 75 are pitted against each other. I've noticed that surprisingly often both teams seem to have the same characters. This got me thinking about how likely this is and since probability has never been my forte I began searching for an answer but was unsuccessful. So I was curious if anyone would have any idea of how to go about calculating this?
General format: if 2 parties pick K random variables from N choices. What is the chances they will have at least one in common?