Question

How many ways can two dice be rolled such that their sum is between 5 and 10 (exclusive)?

Answer 1

There are 16 ways two dice can be rolled such that their sum is between 5 and 10 (exclusive).

Step-by-step explanation:

To find the number of ways two dice can be rolled such that their sum is between 5 and 10 (exclusive), we can use the concept of combinations. For each possible sum (6, 7, 8, or 9), we need to count the number of distinct pairs of numbers on the dice that add up to that sum. Here's how we can do it:

1. For a sum of 6, the possible pairs are (1, 5), (2, 4), and (3, 3). So, there are 3 ways.
2. For a sum of 7, the possible pairs are (1, 6), (2, 5), (3, 4), and (4, 3). So, there are 4 ways.
3. For a sum of 8, the possible pairs are (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2). So, there are 5 ways.
4. For a sum of 9, the possible pairs are (3, 6), (4, 5), (5, 4), and (6, 3). So, there are 4 ways.

Therefore, the total number of ways the two dice can be rolled with a sum between 5 and 10 (exclusive) is 3 + 4 + 5 + 4 = 16.