Addition principle

 

If we have a ways of doing something and b ways of doing another thing and can not do both at the same time, then there are a + b ways to choose one of the actions.

 

Example

A woman has decided to shop at one store today, either in the north part of town or the south part of town. If she visits the north part of town, she either shop at a mall, a furniture store, or a jewelry store (3 ways). If she visits the south part of town, then she either shop at a clothing store or a shoe store (2 ways).

 

There are 3+2=5 possible shops the woman could end up shopping at today.

 

 

Multiplication Principle

 

If there are a ways of doing something and b ways of doing another thing, then  a · b ways of  doing both actions.

 

Example

 

When you order pizza, first choose the type of crust: thin or deep dish (2 choices). Next, choose the topping: cheese, pepperoni, or sausage (3 choices).

 

Using the rule of product, you know that there are 2 × 3 = 6 possible combinations of ordering a pizza.

 

 

Example 2

How many different license plates can be made if each plate contains a sequence of three

uppercase English letters followed by three digits?

 

There are 26 choices for each of the three uppercase English letters and ten choices for
each of the three digits. There are a total of 26 • 26 • 26 • 10 • 10 • 10 = 17,576,000 possible license plates.