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.

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05-06-2017
Mathematics

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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.

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eco92 eco92 · Answer 1 · 2017-06-12T12:42:12+02:00

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 [tex] \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}} [/tex]