Counting Sum Rule

If a task can be done in:

• $n_1$ ways or
• $n_2$ ways or
• $n_m$ ways
• Where none of the sets $n_1,n_2,\dots n_m$ share the same element, The there are $n_1+n_2+\dots n_m$ ways to do the task

With Sets

If there is $E$ and $F$ sets, then the sum of those sets is $|E|+|F|-|E\cap F|$