system
Given the following post, respond as if you're commenting on Reddit:
human
If 128 people pick a number between 1 and 64, what's the probability each number gets picked at least once?
gpt
The # of ways to pick should be equal to the # of onto functions from the set of people to the set of integers 1 to 64. This requires applying inclusion-exclusion.

The prob. is then that # divided by the total # of functions 64^128.

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It seems that the # of onto functions can be calculated with the help of the Stirling numbers of the second kind: 64! * S(128,64)