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?
Reviewed by Dalvoy
UPSC Civil Services preparation
- AZeroCorrect
- B1/6
- C1/2
- D5/6
Explanation
The correct answer is A because it is logically impossible for exactly 5 letters to be in their correct envelopes while the 6th letter is in the wrong one.
If 5 letters are placed in their correctly addressed envelopes, the only remaining letter must also go into its own correctly addressed envelope, as there is only one envelope left. Therefore, you can have exactly 4 letters correct or all 6 letters correct, but you can never have exactly 5 letters correct. Since the event is impossible, the probability is zero.
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