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In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of $n$ randomly chosen people, some pair of them will have the same birthday.
15
votes
How many numbers can I generate and be 90% sure that there are no duplicates?
The other answer uses an approximation. Here is an answer with an exact formula.
The probability that there are no duplicates when drawing $k$ numbers among $N=10000$ is :
$$P_{N,k} = \frac{\text{numb …