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You and your friend are two of eight servers working a shift in a restaurant. At the beginning of the shift, the manager randomly assigns one section to each server. Find the probability that you are assigned Section 1 and your friend is assigned Section 2. Express you answer as a fraction in simplest form.The probability is .

Question

You and your friend are two of eight servers working a shift in a restaurant. At the beginning of the shift, the manager randomly assigns one section to each server. Find the probability that you are assigned Section 1 and your friend is assigned Section 2. Express you answer as a fraction in simplest form.The probability is .

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Solution

To solve this problem, we need to understand that the assignment of sections to servers is a random process. There are 8 sections and 8 servers, so each server has an equal chance of being assigned any section.

Step 1: Calculate the probability of you being assigned Section 1. Since there are 8 sections, the probability is 1/8.

Step 2: Now, assuming you have been assigned Section 1, there are now 7 sections left for the remaining 7 servers. So, the probability of your friend being assigned Section 2 is 1/7.

Step 3: The overall probability of both events happening is the product of their individual probabilities. So, the probability of you being assigned Section 1 and your friend being assigned Section 2 is (1/8) * (1/7) = 1/56.

So, the probability is 1/56.

This problem has been solved

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