A flag has to be designed with 4 horizontal stripes using some or all of the colours red, green and yellow. What is the number of different ways in which this can be done so that no two adjacent stripes have the same colour?
Answer & explanation
Answer: (c) 24
The top stripe can take any of 3 colours, and each later stripe any colour except the one just above it (2 choices). So there are 3 × 2 × 2 × 2 = 24 flags.
- Stripe 1: 3 choices.
- Stripes 2, 3 and 4: each must differ from the stripe above it, so 2 choices each.
- Total = 3 × 2 × 2 × 2 = 24.
- 'Some or all of the colours' allows two-colour flags such as red-green-red-green; they are already included.
Remember · For 'no two adjacent alike', choose the first freely, then (colours − 1) for each next item.
Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·