Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 22 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Amanda, and Bryan are chosen? Enter a fraction or round your answer to 4 decimal places, if necessary. Answer

Step 1 ：The problem is asking for the probability of a specific event in a sample space. The event is that you, Amanda, and Bryan are chosen. The sample space is all possible ways to choose 3 people out of 22.

Step 2 ：The number of ways to choose 3 people out of 22 is given by the combination formula \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.

Step 3 ：Here, n = 22 and k = 3. So, the total number of combinations is 1540.

Step 4 ：The event of choosing you, Amanda, and Bryan is a specific combination, so there is only 1 way this can happen.

Step 5 ：Therefore, the probability is given by the ratio of the number of ways the event can occur to the total number of outcomes in the sample space.

Step 6 ：So, the probability is \(\frac{1}{1540}\) which is approximately 0.0006.

Step 7 ：Final Answer: The probability that you, Amanda, and Bryan are chosen is \(\boxed{0.0006}\) or \(\boxed{\frac{1}{1540}}\) in fraction form.