Suppose that your boss must choose four employees in your office to attend a conference in Jamaica. Because all 11
 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, Christofer, Samantha, and David are chosen? Enter a fraction or round your answer to 4
 decimal places, if necessary.


To determine the probability of selecting you, Christofer, Samantha, and David to attend the conference, we need to calculate the total number of ways to select 4 employees from the 11 people in the office, and then identify how many of those selections involve exactly you, Christofer, Samantha, and David.

### Step 1: Total number of ways to choose 4 employees out of 11
The total number of ways to choose 4 employees from 11 is given by the combination formula:

\[
\text{Number of ways} = \binom{11}{4} = \frac{11!}{4!(11-4)!} = \frac{11!}{4! \cdot 7!}
\]

\[
= \frac{11 \times 10 \times 9 \times 8}{4 \times 3 \times 2 \times 1} = 330
\]

So, there are 330 possible ways to choose 4 employees from 11.

### Step 2: Favorable outcome
There is only **1** favorable outcome, which is the selection of you, Christofer, Samantha, and David.

### Step 3: Probability calculation
The probability is the ratio of favorable outcomes to the total number of possible outcomes:

\[
\text{Probability} = \frac{1}{330}
\]

### Final Answer
The probability that you, Christofer, Samantha, and David are chosen is:

\[
\frac{1}{330} \approx 0.0030
\]

So, the probability is approximately **0.0030**.

Would you like more details on combinations or have any questions?

Here are 5 related questions to explore:
1. How do you calculate combinations for choosing teams of different sizes?
2. What is the probability of you being chosen if you add more employees to the group?
3. What is the difference between combinations and permutations?
4. How does the probability change if the boss decides to choose 5 people instead of 4?
5. How do probabilities apply when selections are not random?

**Tip:** When dealing with combinations, remember that the order of selection does not matter.

Suppose that your boss must choose four employees in your office to attend a conference in Jamaica. Because all 11 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, Christofer, Samantha, and David are chosen? Enter a fraction or round your answer to 4 decimal places, if necessary.

Learn how to calculate the probability of selecting 4 specific employees out of 11 for a conference. This problem demonstrates the use of combinations and probability formulas to solve real-world scenarios. Suitable for students in Grades 9-11.

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