A person writes four letters and address four envelopes. If the letters are placed in the envelopes at random, then the probability that not all letters are placed in the right envelope is

Step-by-step solution

The total number of ways to place 4 letters into 4 envelopes is 4! = 24 . The event that all letters are placed in the right envelope corresponds to exactly 1 way (each letter in its corresponding envelope). The probability that all letters are placed in the right envelope is P(A) = 1 24 . The probability that not all letters are placed in the right envelope is the complement of the event that all letters are placed correctly. Therefore, the required probability is 1 - P(A) = 1 - 1 24 = 23 24 . Answer: 23 24