My question was inspired by this numberphile video on the maths of secret santa.
So suppose you have a group of n people who are all randomly choosing another person in the group at random. The probability the any given person chooses themselves is p = 1/n and the expected value of X (the number of people who choose themselves) is equal to np = n * 1/n = 1. If someone(s) chooses themselves, then everyone has to choose another person at random again.
Let's define the random variable Y as the number of attempts the group will have to make until everyone chooses someone who is not themselves.
My question is, find the expected value of Y, E(Y).
I didn't know how to compute this mathematically but When ran a bunch of simulations I found that the answer rounded to e (2.71828...)!
Can someone please explain why e is showing up here.
from Hot Weekly Questions - Mathematics Stack Exchange
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