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 ?
- (a) 12
- (b) 18
- (c) 24 ✓ UPSC's answer
- (d) 36
Why the answer is (c)
• The first stripe can be any of the 3 colours.
• Each later stripe must differ from the one just above it, leaving 2 choices each for stripes 2, 3 and 4.
• Total = 3 × 2 × 2 × 2 = 24.
• ('Some or all' colours is automatically satisfied, since at least two colours are always used.) Hence option (c).
Why the other options are wrong
- (a) 12
- 12 = 3 × 2 × 2 counts only three stripes; the flag has four.
- (b) 18
- 18 does not match 3 × 2 × 2 × 2.
- (d) 36
- 36 ignores the rule for at least one pair of adjacent stripes.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2023, held on 28 May 2023. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.