# Q. A, B and C are three places such that there are three different roads from A to B, four different roads from B to C and three different roads from A to C. In how many different ways can one travel from A to C using these roads?

a. 10

b. 13

c. 15

d. 36

Correct Answer: c. 15

#### Question from UPSC Prelims 2022 CSAT Paper

**Explanation : **

## A B C are three places

One can travel from A to C in 15 different ways. There are two possible routes: directly from A to C or from A to B and then from B to C.

The **number of ways to travel directly from A to C is 3** (since there are 3 different roads). The number of ways to travel from **A to B** and then from **B to C** is the product of the number of roads between each pair of places: **3 x 4 = 12**.

So, in total, there are** 3 + 12 = 15** different ways one can travel from A to C using these roads.