373.The Missing Seven
★★★classical probabilityCh. 1 — Classical Probability and Combinatorics444+ Problems in Probability
7 people each independently select a uniformly random integer from . Given that nobody selected 7, find the probability that 7 is the only value nobody selected.
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Conditioned on avoiding 7, the picks are IID uniform on — so you need the probability that 7 draws cover all 6 values (count surjections).
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