107.Age Order at a Round Table
★★★classical probabilityCh. 1 — Classical Probability and Combinatorics444+ Problems in Probability
7 people sit around a circular table uniformly at random. All of them have distinct ages. Find the probability that they sit in age order around the table. The ages can be increasing in either the clockwise or counter-clockwise direction.
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Fix the youngest person's seat — how many arrangements of the rest are in order?
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