Addition Principle

The Addition Principle says that if one task can be done in \( m \) ways and another task in \( n \) ways, then there are \( m + n \) ways to do either task.

We use the Addition Principle when choices are mutually exclusive and cannot happen at the same time.

Examples:

• If there are $3$ different cakes and $4$ different mousses on the menu, you have \( 3 + 4 = 7 \) total dessert choices.
• A college student is required to take $1$ college class from a group of $5$ math and $3$ computer science courses, so there are \( 5 + 3 = 8 \) options in total.

It is important that the choices are separate and do not overlap.

If choices can overlap, we will need to adjust our counting to avoid double-counting: see the next slide.