Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 17
 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, Olivia, and Liam are chosen? Enter a fraction or round your answer to 4
 decimal places, if necessary.

To find the probability that you, Olivia, and Liam are chosen from a group of 17 people, we can follow these steps:

1. **Total number of ways to choose 3 people from 17**: 
   This is calculated using combinations since the order in which people are chosen doesn't matter. The formula for combinations is:

   \[
   \binom{n}{r} = \frac{n!}{r!(n-r)!}
   \]
   where \( n = 17 \) and \( r = 3 \). So, the total number of ways to choose 3 people from 17 is:

   \[
   \binom{17}{3} = \frac{17!}{3!(17-3)!} = \frac{17 \times 16 \times 15}{3 \times 2 \times 1} = 680
   \]

2. **Number of favorable outcomes**: 
   There's only 1 specific way to choose you, Olivia, and Liam from the group of 17, since we are fixing these 3 people.

3. **Probability calculation**: 
   The probability is the number of favorable outcomes divided by the total number of possible outcomes:

   \[
   P = \frac{1}{680}
   \]

So, the probability that you, Olivia, and Liam are chosen is \( \frac{1}{680} \), or approximately 0.0015 when rounded to 4 decimal places.

### Final Answer:
\[
\text{Probability} = \frac{1}{680} \approx 0.0015
\]

Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:
1. What if there were 20 people instead of 17? How would the probability change?
2. How would the calculation change if 4 employees were chosen instead of 3?
3. What is the probability of not being chosen in a random draw from this group?
4. How does the formula for combinations work for larger groups, such as 100 employees?
5. If Olivia and Liam are chosen but not you, what is the probability of this event?

**Tip:** In probability problems, always make sure to distinguish between combinations and permutations. Combinations ignore the order, while permutations consider it!

Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 17 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, Olivia, and Liam are chosen? Enter a fraction or round your answer to 4 decimal places, if necessary.

Learn how to calculate the probability of selecting you, Olivia, and Liam out of 17 employees using combinatorics and probability. This problem involves the combination formula and basic probability principles. Suitable for high school students in Grades 9-12.

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