Addition principle

In combinatorics, the rule of sum is a basic counting principle. Stated simply, it is the idea that if we have a ways of doing something and b ways of doing another thing and we can not do both at the same time, then there are a+b ways to choose one of the actions.

More formally, the rule of sum is a fact about set theory. It states that sum of the sizes of a finite collection of pairwise disjoint sets is the size of the union of these sets. That is, if $S_{1},S_{2},...,S_{n}$ are pairwise disjoint sets, then we have:

$|S_{1}|+|S_{2}|+\cdots +|S_{n}|=|S_{1}\cup S_{2}\cup \cdots \cup S_{n}|$