UPSC Prelims 2017 · CSAT
Question 57: Basic Numeracy
If 2 boys and 2 girls are to be arranged in a row so that the girls are not next to each other, how many possible arrangements are there?
AnswerUPSC’s answer is (c).
Treat the two boys and two girls as different people. Total arrangements: 4! = 24. Girls together: treat them as one block, giving 3! x 2! = 12. So arrangements with girls apart: 24 - 12 = 12. Check by gaps: arrange the boys in 2 ways, leaving 3 gaps; the girls take 2 of them in 3 x 2 = 6 ways, so 2 x 6 = 12.
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) 3 treats people of the same sex as identical, which the question does not.
- (b) 6 counts only the girls' placements, not the boys' arrangements.
- (c) Correct: 24 - 12 = 12.
- (d) 24 includes the arrangements with the girls next to each other.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2017, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.