UPSC Prelims 2008 · General Studies
Question 148: Basic Numeracy
There are 6 different letters and 6 correspondingly addressed envelopes. If the letters are randomly put in the envelopes, what is the probability that exactly 5 letters go into the correctly addressed envelopes?
AnswerThe answer is (a).
If five letters go into their correct envelopes, the sixth letter has only one envelope left, and that is its own. So exactly five correct is impossible: either all six are correct or at most four are. The probability of exactly five correct is therefore zero. Of the 6! = 720 ways, none has exactly five in place.
Why each option is right or wrong
- (a) Zero, since five correct forces the sixth to be correct too.
- (b) 1/6 would need exactly five correct to be possible, which it is not.
- (c) 1/2 is far too high.
- (d) 5/6 is far too high.
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.