## Archive of posts on May 9, 2023

### The distribution when indistinguishable balls are put into boxes

Suppose there are $n$ distinguishable boxes and $k$ indistinguishable balls. Now, we randomly put the balls into the boxes. For each of the boxes, what is the probability that it contains $m$ balls? This is a simple combanitorics problem that can be solved by the stars and bars method. It turns out that in the limit $n,k\to\infty$ with $k/n$ fixed, the distribution tends to be a geometric distribution.

- Categories: math
- Tags: probability, combinatorics, ruby