Title states an example, I'll give the general case question then repeat an example. I have N images and plan to randomly pick k of the possible N images into a set. The order does not matter. I repeat for T trials. What is the chance that any of the k-image sets are repeated at least once across the T trials? More specifically, I have 20 images and plan to randomly pick 10 of the possible 20 images into a set. The order does not matter. I repeat this for 100 trials. What is the chance that any 10-image sets are repeated at least once across the 100 trials?
I realize this is similar to the Birthday problem, however I believe in that problem N equals T. Could be wrong...