Question

A clerk has 4 different letters that need to go in 4 different envelopes. What is the probability that all 4 letters are placed in the correct envelopes?

Answer 1

The probability that all `4` letters are placed in the correct envelopes is `1/24`.

Explanation:

Let us first question how many ways are there in which we can place `4` letters in `4` different envelopes.

The answer is `color(white) - ^4P_4=4xx3xx2xx=24`.

But there is only one way of pacing letters in correct envelopes, of course assuming that addressees areall different.There are

Hence, the probability that all `4` letters are placed in the correct envelopes is `1/24`.