Skip to content

Fundamental Counting Principle

Before learning about probability, it helps to learn about what is known as the ‘fundamental counting principle, and observe some fundamental counting principle examples.

It is something that is useful when you want to work out the number of possible combinations from a selection of different choices/outcomes.

Fundamental Counting Principle

If there were   “a”   possible ways of performing one action,

and   “b”   possible ways of performing a second action,

then there would be   a × b   ways of performing  ‘both’  actions together.

This principle can often be especially helpful when dealing with probability, as we area able establish how many outcomes may be possible with certain events.

Provided that the outcome or options are “independent” of each other, and choosing one option wouldn’t have an affect the other.

Fundamental Counting Principle Examples


Image of clothes selection to show the Fundamental Counting Principle
Let’s say a person is getting dressed in the morning.

For the shirt they can wear a  “RED”  shirt or a  “GREEN”  shirt.
( 2  possible choices )

For the trousers they can wear  “BLACK”  or  “WHITE”  or  “BLUE”  trousers.
( 3  possible choices )

The first action  a,  is to choose the shirt colour.
The second action  b,  is to choose the trouser colour.

a × b   =   2 × 3   =   6

There are  6  combinations that can be made in the ways to choose the colour of the shirt and trousers.

Red Shirt with White Trousers   |   Red Shirt with Black Trousers   |   Red Shirt with Blue Trousers

Green Shirt with White Trousers   |   Green Shirt with Black Trousers   |   Green Shirt with Blue Trousers


The fundamental counting principle can also be used when there are more than  2  different events happening.

A boy wants to buy  3  video games at a shop.

They want to buy:

a   “SOCCER”   game,
a   “SHOOTING”   game,
and a   “SIMULATION”   game.

At the shop there is a selection of:

4  Soccer games   ,   12  Shooter games   ,   8  Simulation games.

Of these options, how many combinations of games can be selected?

This case with video game is similar to example  (1.1),  but this time there are  3  events happening,  3  different video game options being selected together.

So instead of   a × b,   we will have   a × b × c.

4  ways to select a Soccer game   ( a )
12  ways to select a Shooting game   ( b )
8  ways to select a Simulation game   ( c )

a × b × c   =   4 × 12 × 8   =   384

There are  384  combinations of the  3  video game selections specified in the shop, when the boy buys a separate “Soccer”, “Shooting” and “Simulation” game together.

  1. Home
  2.  ›
  3. Probability and Statistics
  4. › Fundamental Counting Principle

Return to TOP of page