# 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?

Jun 13, 2017

The probability that all $4$ letters are placed in the correct envelopes is $\frac{1}{24}$.

#### Explanation:

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

The answer is ${\textcolor{w h i t e}{-}}^{4} {P}_{4} = 4 \times 3 \times 2 \times = 24$.

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 $\frac{1}{24}$.