A mail-sorting clerk is given 4 envelopes addressed to different people and 4 letters. She has to carefully put the letters in the correct envelopes and then mail them. However, she carelessly puts any letter in any envelope, making sure that each envelope has precisely one of those 4 letters. What is the likelihood that all the letters are in the correct envelope?

A

$$\frac{1}{24}$$

B

$$\frac{1}{12}$$

C

$$\frac{1}{6}$$

D

$$\frac{1}{4}$$