Question

If n letters are placed into n addressed envelopes at random, the probability that at least one letter will go into a wrongly addressed envelope is

A.1/n
B.n−1/n
C.1−1/n!
D.1/n!

Answer 1

The probability that at least one letter will end up in a wrongly addressed envelope when 'n' letters are randomly placed into 'n' envelopes is calculated by subtracting the probability of all being correctly addressed (1/n!) from 1, giving 1 - 1/n! (option C) as the answer.

Step-by-step explanation:

The question involves calculating the probability that at least one letter will end up in a wrongly addressed envelope when 'n' letters are placed into 'n' addressed envelopes at random. One way to answer this question is to subtract the probability of all letters being correctly addressed from the total probability (which is 1).


The probability of all letters being correctly addressed is the number of successful ways to arrange the letters (which is 1, as there's only one correct arrangement) divided by the total number of possible arrangements, which is 'n!' (read as 'n factorial'). Therefore, the probability of all letters being correctly addressed is 1/n!. As such, the probability of having at least one letter in a wrong envelope is given by:

1 - (1/n!)

Thus, the correct answer to the student's question is option C: 1 - 1/n!.