## Quick Reference

An intriguing probability problem. At a birthday party *n* children are given hats. The hats are later shuffled and randomly reassigned. The probability that exactly *k* get the same hat twice is . As *n* increases, this probability approaches (1/*k*!)e^{−1}. The probability that none gets the same hat twice approaches e^{−1}≈0.368. Note that the result for *n*=5 is 0.367, so that the probability of no matches is essentially the same whether there are 5 or 500 children.

**From:**
hat matching
in
A Dictionary of Statistics »

*Subjects:*
Probability and Statistics.