## Fundamental principle of counting

The Fundamental principle of counting (or Multiplication principle) states that:
"If an event can occur in $m$ different ways, following which another event can occur in $n$ different ways, then the total number of occurrence of the events in the given order is $m \times n$."

Example:
If you have 3 trousers and 2 shirts, in how many ways can you dress up?

Soln. In order to dress up, you will have to select a trouser and a shirt each. Since you have 3 trousers, you can select a trouser in 3 ways. Similarly, you can select a shirt in 2 ways.
Now, as per the multiplication principle, the total number of ways in which you can select a trouser as well as a shirt is $3 \times 2 = 6$. So, you can dress up in 6 different ways.
"If an event can occur in $m$ different ways, following which another event can occur in $n$ different ways, following which a third event can occur in $p$ different ways, then the total number of occurrence to the events in the given order is $m \times n \times p$."