Fundamental Counting Principle

Fundamental Counting Principle

The Fundamental Counting Principle helps you find how many total outcomes are possible when a task is done in stages. If one step can be done in a ways and a second step can be done in b ways, then the total number of outcomes is a × b. For more steps, keep multiplying the number of choices for each step.

How to solve

1. Identify each stage of the situation.
2. Count the number of choices for each stage.
3. Multiply the counts together.
4. Simplify the result if needed.

Important idea

Each choice in one stage combines with every choice in the next stage. That is why multiplication is used instead of addition.

Example pattern

If a shirt can be chosen in 3 colors and pants in 4 styles, then the total number of outfits is:

3 × 4 = 12

Check your answer

Make sure your final number makes sense. If you list a few outcomes, you should see that each choice from one stage pairs with all choices from the others. Also, verify that you did not add when the steps are independent and sequential.