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.