## 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.

(Answer: 6)

The above principle can be generalised for any finite number of events.

For example, for 3 events, the principle is as follows:

"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 $m \times n \times p$."

**Practice:**

Exercise 1 (Bike purchase)