Nice, this problem is isomorphic to the probability/graph theory problem “hunters and rabbits” from Matousek’s discrete math textbook, except with the slight modification that instead of “n hunters with perfect accuracy each randomly and simultaneously shoot one rabbit among a set of m rabbits”, it’s “n birthday havers each simultaneously have a birthday among m=365 days”
There is a closed form solution to this problem’s expectation for arbitrary n and m, which I’ve linked below:
There is a closed form solution to this problem’s expectation for arbitrary n and m, which I’ve linked below:
https://math.stackexchange.com/questions/610250/a-question-o...