There are five unmarked envelopes on a table, each with a letter for a different person. If the mail is randomly distributed to these five people, with each person getting one letter, what is the probability that exactly four people get the right letter?
If these five letters are each intended for the five persons (one per person), then, with random distribution, it is impossible for exactly four of the persons to get the correct letter. If each of the four persons get the letters intended for him/her, then the fifth person will get the letter intended for him/her.
The probability is zero.