Two distinct dice are thrown. We need to find the number of possible outcomes where the sum of the numbers on the two dice is equal to 5 or 6.

1. Problem Description

Two distinct dice are thrown. We need to find the number of possible outcomes where the sum of the numbers on the two dice is equal to 5 or

6.

2. Solution Steps

Let the numbers on the two dice be $x$ and $y$.

The possible values for $x$ and $y$ are $1, 2, 3, 4, 5, 6$. Since the dice are distinct, the order of the numbers matters.

Case 1: The sum is

5. We need to find pairs $(x, y)$ such that $x + y = 5$.

The possible pairs are $(1, 4), (2, 3), (3, 2), (4, 1)$.

So, there are 4 possible outcomes where the sum is

5.

Case 2: The sum is

6. We need to find pairs $(x, y)$ such that $x + y = 6$.

The possible pairs are $(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)$.

So, there are 5 possible outcomes where the sum is

6.

Since the two cases (sum is 5 or sum is 6) are mutually exclusive, we can add the number of outcomes in each case.

Total number of outcomes = Number of outcomes where the sum is 5 + Number of outcomes where the sum is 6

Total number of outcomes = $4 + 5 = 9$

3. Final Answer

The number of possible outcomes is 9.