UPSC Prelims 2005 · General Studies
Question 103: Basic Numeracy
2 men and 1 woman board a bus in which 5 seats are vacant. One of these five seats is reserved for ladies. A woman may or may not sit on the seat reserved for ladies but a man can not sit on the seat reserved for ladies. In how many different ways can the five seats be occupied by these three passengers?
AnswerThe answer is (b).
Seat the woman first. If she takes the ladies' seat, the two men fill 2 of the other 4 seats in 4 × 3 = 12 ways. If she takes one of the 4 ordinary seats (4 ways), the men can use only the 3 remaining ordinary seats, in 3 × 2 = 6 ways, giving 24. Total 12 + 24 = 36.
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) 15 undercounts the seatings.
- (b) Correct: 12 + 24 = 36.
- (c) 48 overcounts: men cannot use the ladies' seat.
- (d) 60 overcounts: men cannot use the ladies' seat.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2005, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.