# Discrete Fubini’s Principle

Sums and products can be written compactly using $\sum$ and $\prod$ notation, but it is sometimes possible to write the same sum or product in more than one way. The so-called discrete Fubini’s principle is a powerful method of exchanging the order in which the indices occur in a nested sum or product. It is so useful that some mathematicians call it their main “trick.”