Rule of Sum


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 A and B which can occur in n and m possible ways, and the events cannot occur simultaneously, then Aor B can occur in m + n 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:

|S_1| + |S_2| + ... + |S_n| = |S_1 \cup S_2 \cup ... \cup S_n|

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