Question:
A, B and C are three cities. There are 5 routes from A to B and 3 routes from B to C. How many different routes are there from A to C via B?
Solution:
Given: 5 routes from A to B and 3 routes from B to C.
To find: number of different routes from $A$ to $C$ via $B$.
Let $E_{1}$ be the event : 5 routes from A to B
Let $E_{2}$ be the event : 3 routes from $B$ to $C$
Since going from $A$ to $C$ via $B$ is only possible if both the events $E_{1}$ and $E_{2}$ occur simultaneously.
So there are $5 \times 3=15$ different routes from $A$ to $C$ via $B$.