**SUM RULE** If an event can occur in $m$ ways and another event can occur in $n$ ways, and if these two events cannot occur simultaneously, then one of the two events can occur in $m+n$ ways. More generally, if $E_i(i=1,2, \ldots, k)$ are $k$ events such that no two of them can occur at the same time, and if $E_i$ can occur in $n_i$ ways, then one of the $k$ events can occur in $n_1+n_2+\cdots+n_k$ ways.

**Example 1.** If there are 18 boys and 12 girls in a class, there are $18+12=30$ ways of selecting 1 student (either a boy or a girl) as class representative.

**Example 2.** Suppose $E$ is the event of selecting a prime number less than 10 and $F$ is the event of selecting an even number less than 10 . Then $E$ can happen in 4 ways, and $F$ can happen in 4 ways. But, because 2 is an even prime, $E$ or $F$ can happen in only $4+4-1=7$ ways.