Question

A company has 25 employees. One day, 8 letters that did not have names on the envelopes arrived for 8 different employees. The mail sorter placed each letter randomly in a different employee's mailbox.

Answer 1

1. The missing question here is : "what is the probability that the mail sorter placed each letter correctly"?

2. Name the letters L1, L2, ....L8   (Letter 1, Letter 2.... Letter 8)

3. The first letter has a probability of 1/25 to be placed in the correct mailbox.

Each of the remaining 7 letters have 1/25 probability, and these probabilities are related.

4. So the probability that each letter goes to the proper mailbox is $\frac{1}{25}* \frac{1}{25}* \frac{1}{25}* \frac{1}{25}* \frac{1}{25}* \frac{1}{25}* \frac{1}{25}* \frac{1}{25}= \frac{1}{ 25^{8}}$