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In combinatorics, the rule of sum or addition principle is a basic counting principle. Stated simply, it is the intuitive idea that if we have A number of ways of doing something and B number of 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 {\displaystyle S_{1},S_{2},...,S_{n}} are pairwise disjoint sets, then we have:
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