Fundamental counting principle

Definition

Fundamental counting principle states that "If an event can occur in 'm' number of different ways, and, if after the occurrence of the event, a second event can occur in 'n' number of different ways, then the total number of different ways in which both the events can occur is m x n

Explanation with an example

The fundamental counting principle tells us the different number of ways in which two events can occur one after the other.

Let us take the example of two coins tossed together. On tossing one coin, either of two events can occur: either we can get heads up, or we can get tails up. Thus, in the above definition, m = 2 (because the event can be either heads or tails - two choices).

After tossing one coin, the other coin is tossed. In this also, two events can occur: either heads or tails. Thus, in the above definition, n = 2.

Now, the total number of different ways in which the two events can occur is given by m x n = 2 x 2 = 4.

Thus, we know that if two coins are tossed together, there can be 4 different results. We can verify it by the table given below:

Coin 1	Coin 2
Heads	Heads
Heads	Tails
Tails	Heads
Tails	Tails

The above table represents the different results obtained when two coins are tossed together. We can see that there are 4 different results, as we obtained by using the Fundamental counting principle without having to list all of them. This is very useful when there are a large number of events.