Question

If four letters are placed into 4 addressed envelopes at random, the probability that exactly one letter will go wrong is

• A. $0$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{1}{4}$

Answer 1

The correct option is A $0$

Total arrangements $=4!=24$
If we put one letter in a wrong envelope, then we cannot manage to keep the other three correct. This is because if other three are put in correct envelopes, then the fourth one is left with the correct envelope too. Hence there is no such case when exactly one of them is correctly placed.
Hence $P=0$