The rule of sum, also sometimes called the sum rule principle or addition principle, is a basic counting principle in combinatronics. It states that if we have two events and which can occur in and possible ways, and the events *cannot* occur simultaneously, then *or* can occur in ways. This rule can be extended to three or more events as long as only one event can occur at a time.

The rule of sum arises from set theory. It formally says that the the cardinality of the union of a group of pairwise disjoint sets is equal to the sum of the cardinalities of each set:

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