UPSC Prelims 2018 · CSAT
Question 62: Basic Numeracy
For a sports meet, a winners' stand comprising three wooden blocks is in the following form :
There are six different colours available to choose from and each of the three wooden blocks is to be painted such that no two of them has the same colour. In how many different ways can the winners' stand be painted?
AnswerUPSC’s answer is (a).
The winners' stand has three blocks, each painted in a different colour from six. The first block can take any of 6 colours, the second any of the remaining 5, the third any of the remaining 4. Total = 6 × 5 × 4 = 120. This is the permutation 6P3, used whenever order matters and repeats are not allowed.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Correct: 6 × 5 × 4 = 120.
- (b) 81 is 3⁴ and does not count ordered choices without repeats.
- (c) 66 does not equal 6 × 5 × 4.
- (d) 36 is 6 × 6, which ignores the rule against repeated colours.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2018, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.