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?
Answer & explanation
Answer: (c) 15
One can go directly from A to C (3 ways) or go through B (3 × 4 = 12 ways). These are alternatives, so they add: 3 + 12 = 15.
- Direct routes from A to C: 3.
- Routes through B: 3 roads from A to B × 4 roads from B to C = 12.
- Total = 3 + 12 = 15.
Remember · Legs taken one after another multiply; alternative routes add.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·