UPSC Prelims 2008 · General Studies
Question 3: Basic Numeracy
In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?
AnswerThe answer is (b).
Four books can be stacked in 4! = 24 ways. Count the arrangements where A and B are together and subtract. Treat A and B as one block: the block and the other two books can be arranged in 3! = 6 ways, and A and B can swap places inside the block in 2 ways, giving 12. So the number of arrangements with A and B never adjacent is 24 - 12 = 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.
This follows an unofficial answer: UPSC has not published its key for this year, and if that answer is wrong, so is this path.
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) 9 does not match the count: 24 total minus 12 adjacent arrangements leaves 12.
- (b) 24 total minus 12 with A and B together leaves 12.
- (c) 14 would need only 10 adjacent arrangements, but there are 12.
- (d) 18 would need only 6 adjacent arrangements; forgetting that A and B can swap inside the block gives this error.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2008, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.