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.