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:
