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?

Question

Philoid · Accepted Answer

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 E₁ be the event : 5 routes from A to B

Let E₂ be the event : 3 routes from B to C

Since going from A to C via B is only possible if both the events E₁ and E₂ occur simultaneously.

So there are 5 × 3=15 different routes from A to C via B.