Fundamental counting principle


We will introduce the fundamental counting principle with an example. This counting principle is all about choices we might make given many possibilities.






Suppose most of your clothes are dirty and you are left with 2 pants and 3 shirts.

How many choices do you have or how many different ways can you dress?

Let's call the pants: pants #1 and pants #2

Let's call the shirts: shirt #1, shirt #2, and shirt #3

Then, a tree diagram as the one below can be used to show all the choices you can make

Tree for the number of ways to wear 2 pants and 3 T-shirts


As you can see on the diagram, you can wear pants #1 with shirt # 1. That's one of your choices.

Count all the branches to see how many choices you have.

Since you have six branches, you have 6 choices.

However, notice that a quick multiplication of 2 × 3 will yield the same answer.

In general, if you have n choices for a first task and m choices for a second task, you have n × m choices for both tasks

In the example above, you have 2 choices for pants and 3 choices for shirts. Thus, you have 2 × 3 choices.



Another example:

You go a restaurant to get some breakfast. The menu says pancakes, waffles, or home fries. And for drink, coffee, juice, hot chocolate, and tea. How many different choices of food and drink do you have?

There 3 choices for food and 4 choices for drink.

Thus, you have a total of 3 × 4 = 12 choices.


A nice fundamental counting principle quiz is given below so you can verify if this lesson is clearly understood.





Recent Articles

  1. Linear Parent Function

    Nov 20, 17 11:18 AM

    What is a linear parent function? Crystal clear explanation.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest





Recent Lessons

  1. Linear Parent Function

    Nov 20, 17 11:18 AM

    What is a linear parent function? Crystal clear explanation.

    Read More

  Our Top Pages

Formula for percentage

Compatible numbers

Basic math test

Basic math formulas

Types of angles

Math problem solver

Algebra word problems

Surface area of a cube

Finding the average 

Scale drawings

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 


Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.

 Recommended

Scientific Notation Quiz

Types of Angles Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz