https://file.aiquickdraw.com/mathbot/file/17271062321682l5vh1m7.jpg

Let's break down the problem to check if your answer, 0.001, is correct.

### Problem Summary:
- There are **13 students** in total (Kelly, Lynn, Mark, and 10 others).
- There are **3 different prizes** to be awarded.
- We want the probability that **Kelly, Lynn, and Mark** win the three prizes.

### Step-by-Step Approach:

1. **Total number of possible outcomes:**
   The total number of ways to assign the three different prizes to the 13 students is the number of permutations of 13 students taken 3 at a time:
   \[
   P(13, 3) = 13 \times 12 \times 11 = 1716
   \]
   So, there are 1,716 possible ways to assign the three prizes.

2. **Number of favorable outcomes:**
   For Kelly, Lynn, and Mark to win the three prizes, there are exactly 3! (since the prizes are different) ways to assign the prizes to them. This is:
   \[
   3! = 6
   \]
   So, there are 6 favorable outcomes.

3. **Probability calculation:**
   The probability is the number of favorable outcomes divided by the total number of possible outcomes:
   \[
   P = \frac{6}{1716} = 0.0035
   \]

### Conclusion:
The correct probability, to the nearest thousandth, is **0.004**, not 0.001.

Let me know if you need further clarification or more details. 

Here are 5 related questions:
1. How would the probability change if there were 20 students in total?
2. What if the prizes were identical instead of different?
3. How do you calculate combinations and permutations?
4. What is the probability if we wanted only Kelly and Mark to win two of the three prizes?
5. How would the probability change if there were 5 prizes instead of 3?

**Tip:** Remember that for problems involving ordered selections (like different prizes), you use permutations, but for unordered selections (like identical prizes), you use combinations.

Three prizes are rewarded in a raffle during a halftime show at a school basketball game. Kelly, Lynn, Mark, and 10 other students each have one ticket. If the three prizes are different and have different values, what is the probability that Kelly, Lynn, and Mark win the three prizes?

Calculate the probability that Kelly, Lynn, and Mark win three different prizes in a raffle, using permutation and probability formulas. This problem covers key concepts in probability theory and is suitable for students in Grades 9-12.

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