The question asks to determine how many of the 36 possible outcomes (when rolling two dice) result in a sum between 2 and 9, inclusive.

Let's analyze:

Possible sums with two dice:

1. Sum = 2: (1,1)
2. Sum = 3: (1,2), (2,1)
3. Sum = 4: (1,3), (2,2), (3,1)
4. Sum = 5: (1,4), (2,3), (3,2), (4,1)
5. Sum = 6: (1,5), (2,4), (3,3), (4,2), (5,1)
6. Sum = 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
7. Sum = 8: (2,6), (3,5), (4,4), (5,3), (6,2)
8. Sum = 9: (3,6), (4,5), (5,4), (6,3)

Total favorable outcomes:

• Sum 2: 1 outcome
• Sum 3: 2 outcomes
• Sum 4: 3 outcomes
• Sum 5: 4 outcomes
• Sum 6: 5 outcomes
• Sum 7: 6 outcomes
• Sum 8: 5 outcomes
• Sum 9: 4 outcomes

Adding these, we get: $1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 = 30$

Thus, there are 30 different ways the sum of the two dice can be between 2 and 9, inclusive.

Would you like further details or have any questions? Here are 5 related questions for you:

1. How many possible outcomes are there in total when rolling two dice?
2. What is the probability of getting a sum between 2 and 9?
3. What are the outcomes for a sum of exactly 10 or higher?
4. How do we calculate the total probability space for rolling two dice?
5. Can you list all outcomes that give an odd sum?

Tip: When calculating probabilities, always divide the favorable outcomes by the total number of possible outcomes to get a fraction.