# The Sum Rule

Suppose that A and B are two disjoint events, that is, they never occur together. Further, suppose that A occurs in m ways and B occurs in n ways. Then A or B can occur in m + n ways. This rule can be extended to more than two mutually exclusive events. Suppose you have 5 full-sleeves and 7 half-sleeves shirts. In how many ways can you wear a shirt? Since you have 5 + 7 = 12 shirts and you are going to wear exactly one shirt, you can wear a shirt in 5 + 7 = 12 ways. If in addition to 5 full-sleeves and 7 half-sleeves shirts, you have 8 T-shirts, then the number of ways in which you can wear a shirt out of these is 5 + 7 + 8 = 20 ways. The above illustration explains a general principle, called the sum rule.

**Illustration**

**Toy Shop**