Department of Mathematics
Undergraduate Problem Solving Competition

Problem 1 (9/30 - 10/14) - Airplane seats

Solution 1a (PDF) | Solution 1b (PDF)

a) There are four people boarding a plane. Each person has a sequentially numbered ticket, and the people board the plane one at a time in the order of their tickets (ie., the first person on board has a ticket for seat 1, the second person for seat 2, and so on). The first person on the plane sits in a random seat - possibly his own - with equal probability to each seat. Everyone else will sit in their assigned seat if it is open, but will sit in a random seat, equal probability to all remaining open seats, if they are displaced. What's the probability that the last person on the plane gets his seat?

b) What about if there are 10 people and 10 seats on the plane?

c) n people, n seats?

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