The sum rule
The sum rule. If a first task can be done in n ways and a second task
can be done in m ways, and these tasks cannot be done using the same
way, then there are n+m ways to do either task.
Example. The department should send, as a representative to a
university committee, either a faculty member (first task), or a student
If there are 13 faculty members and 47 students, then there are
13+47=60 ways to send a representative to the committee.
! Notice that this would not be true if one of the faculty members is,
at the same time, a student.