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 ✓ UPSC's answer
- (d) 36
Why the answer is (c)
• Direct travel from A to C is possible via 3 distinct roads.
• Indirect travel from A to C via B involves choosing one of the 3 roads from A to B and one of the 4 roads from B to C.
• The number of indirect routes is calculated as 3 (A to B) multiplied by 4 (B to C), which equals 12.
• The total number of ways to travel from A to C is the sum of direct and indirect routes: 3 + 12 = 15.
• Therefore, the correct option is (c).
Why the other options are wrong
- (a) 10
- Option (a) is incorrect because it likely sums the number of roads (3+4+3) without accounting for the combinations of indirect paths.
- (b) 13
- Option (b) is incorrect because it does not match the calculated total of 15 distinct routes.
- (d) 36
- Option (d) is incorrect because it multiplies all road counts (3*4*3) instead of adding the direct and indirect path combinations.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.