In combinatorics, the rule of sum is a basic counting principle. Stated simply, it is the idea that if we have ways of doing something and ways of doing another thing and we can not do both at the same time, then there are 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 are pairwise disjoint sets, then we have: