The image presents a table of outcomes from rolling two dice, with a question asking how many possible sums fall between 5 and 12 inclusive.

To solve this, we need to count how many of these pairs from the table give a sum in the range from 5 to 12.

Here’s the breakdown of the possible sums:

• Sum = 5: (1,4), (2,3), (3,2), (4,1) → 4 outcomes
• Sum = 6: (1,5), (2,4), (3,3), (4,2), (5,1) → 5 outcomes
• Sum = 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 outcomes
• Sum = 8: (2,6), (3,5), (4,4), (5,3), (6,2) → 5 outcomes
• Sum = 9: (3,6), (4,5), (5,4), (6,3) → 4 outcomes
• Sum = 10: (4,6), (5,5), (6,4) → 3 outcomes
• Sum = 11: (5,6), (6,5) → 2 outcomes
• Sum = 12: (6,6) → 1 outcome

Now, summing up all the outcomes: $4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 30$

Thus, there are 30 different ways to get sums between 5 and 12 inclusive.

Would you like any more details or have further questions? Here are five related questions you might find interesting:

1. What is the probability of rolling a sum of 7 with two dice?
2. How many total outcomes are possible when rolling two dice?
3. What is the probability of rolling a sum less than 5 with two dice?
4. How would the answer change if we considered sums between 6 and 10 inclusive?
5. How does the distribution of sums change if we roll three dice instead of two?

Tip: When rolling two dice, the most probable outcome is a sum of 7, as it has the highest number of combinations.