Three dice are rolled once. The chance of getting a score of 5 is:

Options

A. `5/216`
B. `1/6`
C. `1/36`
D. `1/(7^(2))`

Answer

To find the probability of getting a score of 5 when three dice are rolled, we can follow these steps:

### Step 1: Determine the total number of outcomes when rolling three dice.
When rolling a single die, there are 6 possible outcomes (1 through 6). Therefore, when rolling three dice, the total number of outcomes is:
\[ 6 \times 6 \times 6 = 6^3 = 216 \]

### Step 2: Identify the favorable outcomes that sum to 5.
Next, we need to find all the combinations of the three dice that add up to 5. The possible combinations are:
1. (1, 1, 3)
2. (1, 2, 2)
3. (1, 3, 1)
4. (2, 1, 2)
5. (2, 2, 1)
6. (3, 1, 1)

Now, we can list these combinations and count the distinct arrangements:
- (1, 1, 3) can occur in 3 ways: (1, 1, 3), (1, 3, 1), (3, 1, 1)
- (1, 2, 2) can occur in 3 ways: (1, 2, 2), (2, 1, 2), (2, 2, 1)

Thus, the favorable outcomes that sum to 5 are:
1. (1, 1, 3)
2. (1, 2, 2)
3. (3, 1, 1)
4. (2, 1, 2)
5. (2, 2, 1)

Counting these, we have a total of 6 favorable outcomes.

### Step 3: Calculate the probability.
The probability \( P \) of an event is given by the formula:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ P = \frac{6}{216} = \frac{1}{36} \]

### Final Answer:
The probability of getting a score of 5 when rolling three dice is \( \frac{1}{36} \).

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