UPSC Prelims 2022 · CSAT
Question 77: Basic Numeracy
There are 9 cups placed on a table arranged in equal number of rows and columns out of which 6 cups contain coffee and 3 cups contain tea. In how many ways can they be arranged so that each row should contain at least one cup of coffee?
AnswerUPSC’s answer is (d).
Place the 3 tea cups among the 9 spots of the 3 × 3 table: C(9,3) = 84 ways. A row lacks coffee only if all 3 of its cups are tea, which uses all 3 tea cups. That happens for exactly one chosen row, so 3 ways. Valid arrangements = 84 − 3 = 81. Cups of the same drink are treated as identical, so only the positions of the tea cups matter.
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) 18 does not follow from 84 less the 3 bad cases.
- (b) 27 does not follow from 84 less the 3 bad cases.
- (c) 54 does not follow from 84 less the 3 bad cases.
- (d) Correct: 84 − 3 = 81.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.