For problems on the distribution of $m$ distinct or identical balls into $n$ distinct or identical bins, optionally with restrictions.

The *balls in bins* or *balls and bins* problem is one of the basic problems of computer science, with wide-ranging applications including hashing and load balancing. It asks: if $m$ balls are thrown at random into $n$ bins, then:

- What is the probability that there is a bin with at least two balls?
- What is the expected fraction of the bins that are nonempty?
- What is the expected number of balls per nonempty bin?
- What is the expected number of bins with more than one ball?

and so forth.