SECRET SANTA RAFFLE
In the secret santa raffle with N people, some draws are viable (no person gets their own name) and others are not. This naturally raises questions like: how likely is a secret santa raffle to be viable?
If the number of people is N, the probability of a draw being viable is given by the formula:
When the number of people tends to infinity, this probability tends to 1⁄e = 0.367879…
A challenge: what is the probability that exactly one person takes their own name?