Sum Rule

Definition

Sum Rule for Ordered Pairs

If there are $m$ choices for the first action, $n$ choices for the second action, and only one of the actions can be taken, the number of possible choices is $m+n$.

Generalized Sum Rule

Suppose there are $k$ actions, if there are $n_1$ choices for the 1st action, $n_2$ choices for the 2nd action, and so on through $n_k$ actions for the $k$-th action, the number of possible choices for the $k$ actions where only one action can be taken is given by the product of the number of choices, which is $n_1+n_2+\dots +n_k$,