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The problem asks for the probability of rolling a sum of 17 with 5 six-sided dice.

### Step-by-step approach:

1. **Total outcomes**: 
   Each six-sided die has 6 faces, so for 5 dice, the total number of possible outcomes is:
   \[
   6^5 = 7776.
   \]
   So, there are 7,776 possible outcomes in total.

2. **Valid outcomes that sum to 17**:
   To find how many combinations of dice sum to 17, we need to determine how many ways 5 numbers between 1 and 6 can add up to 17. This is a partition problem with restrictions.

   A useful way to calculate this is using generating functions or dynamic programming, but to keep things manageable, we can compute the valid combinations by listing or using combinatorics algorithms.

3. **Computation or lookup**:
   This specific problem (rolling 5 dice and getting a sum of 17) is a known scenario and is precomputed in many resources. The number of combinations that give a sum of 17 is **780**.

4. **Probability**:
   The probability of rolling a sum of 17 with 5 six-sided dice is the ratio of favorable outcomes (780) to the total outcomes (7776):
   \[
   P(\text{sum} = 17) = \frac{780}{7776} \approx 0.1003.
   \]

Thus, the probability is approximately **10.03%**.

Would you like more details or have any specific questions?

Here are 5 related questions you might find interesting:
1. What is the probability of rolling a sum of 18 with 5 six-sided dice?
2. How would the probability change if we used 4 dice instead of 5?
3. What is the expected value of the sum when rolling 5 six-sided dice?
4. How does generating functions help in solving dice probability problems?
5. What is the probability of rolling a sum of 17 with 3 six-sided dice?

**Tip**: When solving dice probability problems, breaking it into combinations and leveraging precomputed tables can save a lot of time.

What is the probability of rolling a sum of 17 with 5 six-sided dice?

Discover how to calculate the probability of rolling a sum of 17 with 5 six-sided dice. This step-by-step guide covers key concepts in probability and combinatorics, with a final probability of approximately 10.03%. Suitable for students in Grades 9-12.

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