UPSC Prelims 2023 · CSAT
Question 66: Basic Numeracy
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 ?
AnswerUPSC’s answer is (c).
The first stripe can be any of 3 colours. Each later stripe can be any colour except that of the stripe above it, so it has 2 choices. Number of flags = 3 x 2 x 2 x 2 = 24. Using fewer than all three colours is allowed, and the rule already includes such flags (for example red, green, red, green).
Why each option is right or wrong
- (a) Wrong: too few; the count is 3 x 2 x 2 x 2.
- (b) Wrong: too few; the count is 3 x 2 x 2 x 2.
- (c) Right: 3 x 2 x 2 x 2 = 24.
- (d) Wrong: it would allow 3 choices for some later stripe.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.