Get the latest information and updates on GPRC’s response to COVID-19
Skip to Main Content
It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results.

Math

The Fundamental Counting Principle

The Fundamental Counting Principle is a method that determines the total number of outcomes of an experiment. The principle states that if there are ways for doing something and ways of doing something else after that, then there are a*b ways of doing both these actions. 

 

Example:  A quiz consists of five questions with "yes" or "no" answers. In how many different ways can one complete the quiz?
The quiz consists of Question 1, Question 2, Question 3, Question 4, and Question 5. Each question has two possible answers, yes or no. Therefore, the number of different ways that one can do the quiz is:

 

Example: In how many different ways you can roll a die and toss a coin?
Rolling a die has six outcomes and tossing a coin has two outcomes. Therefore, one can roll a die and toss a coin is:

 

Example: A bagel shop offers 8 different types of bagels and 15 different types of cream cheese. How many possible combinations of bagel and cream cheese are possible?

 

Example: Anna plays on her school basketball team. The basketball uniform has:
  • three different sweaters: black, red, and blue
  • three different shorts: black, red, and blue.
How many different variations of the basketball uniform can the coach choose from for each game?

 

We can use the tree diagram to solve this problem:

 

We can count the number of branches of the tree diagram which gives us nine as the answer. Or, we can use the fundamental counting principle: there are three choices for sweaters and three choices for shorts which gives a total of nine choices. 
Grande Prairie Campus
10726 - 106 Avenue
Grande Prairie, AB T8V 4C4
Phone: 1-780-539-2939
Email: library@gprc.ab.ca
Fairview Campus
11235-98 Avenue
Fairview,AB T0H 1L0
Phone: 1-780-835-6750
Email: fvlibrary@gprc.ab.ca