Eight people are boarding a small airplane one at a time. Each has an assigned seat,...
Eight people are boarding a small airplane one at a time. Each has an assigned seat, but they do not know their seat numbers. The first person chooses uniformly from the eight seats, the second person chooses uniformly from the seven seats that remain, as so on until all the seats have been chosen. What is the probability that every person gets their assigned seat?
Homework Answers
Probability that every person gets their assigned seat is computed here as:
= Probability that the first person gets his assigned seat * Probability that the second person gets his assigned seat given that the first person got his assigned seat * and so on...
= (1/8)*(1/7)*...(1/2)*(1/1)
= 1/8!
Therefore 1/8! = 1/40320 = 0.000025 is the required probability here.
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