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The problem asks to determine the number of ways the sum of two dice can be between 4 and 8 inclusive, based on the provided table of outcomes for two dice.

Let's calculate the number of outcomes where the sum of the two dice is 4, 5, 6, 7, or 8.

### Summing Possible Outcomes:
1. **Sum = 4**: Possible pairs: (1,3), (2,2), (3,1) → 3 outcomes.
2. **Sum = 5**: Possible pairs: (1,4), (2,3), (3,2), (4,1) → 4 outcomes.
3. **Sum = 6**: Possible pairs: (1,5), (2,4), (3,3), (4,2), (5,1) → 5 outcomes.
4. **Sum = 7**: Possible pairs: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 outcomes.
5. **Sum = 8**: Possible pairs: (2,6), (3,5), (4,4), (5,3), (6,2) → 5 outcomes.

### Total:
- Sum of 4 through 8 = \(3 + 4 + 5 + 6 + 5 = 23\).

Thus, there are **23 different ways** to get a sum between 4 and 8 inclusive.

Would you like more details or have any questions?

### Relative questions:
1. What are the total possible outcomes for rolling two dice?
2. How do you calculate probabilities from the number of outcomes?
3. What is the probability of getting a sum between 4 and 8?
4. Can you determine how many outcomes result in a sum greater than 8?
5. How many outcomes result in sums less than 4?

### Tip:
When solving problems with dice, visualizing the sample space using a table, like the one shown, helps systematically count outcomes.

Refer to the table below. Of the 36 possible outcomes, determine the number for which the sum for both dice is from 4 through 8 inclusive.

Learn how to count the number of outcomes for rolling two dice that result in sums between 4 and 8. This problem involves combinatorics and basic probability concepts, suitable for middle school students (Grades 6-8).

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