An automobile license plate number issued by a certain state has 6 character positions. Each of the first 3 positions contains a single digit from 0 through 9. Each of the last 3 positions contains 1 of the 26 letters of the alphabet. Digits and letters of the alphabet can such license plate number can be made?

Options

A. `36`
B. `46,656`
C. `1,000,000`
D. `17,576,000`

Answer

To find the total number of possible automobile license plate numbers, we need to consider the structure of the license plate, which consists of 6 character positions. The first 3 positions can contain digits (0-9), and the last 3 positions can contain letters (A-Z).

### Step-by-Step Solution:

1. **Identify the options for the first 3 positions (digits)**:
- Each of the first 3 positions can contain any digit from 0 to 9.
- There are 10 possible digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
- Therefore, for each of the first 3 positions, there are 10 choices.

2. **Calculate the total combinations for the first 3 positions**:
- Since there are 3 positions and each position has 10 options, the total combinations for the first 3 positions is:
\[ 10 \times 10 \times 10 = 10^3 = 1000 \]

3. **Identify the options for the last 3 positions (letters)**:
- Each of the last 3 positions can contain any letter from the alphabet (A-Z).
- There are 26 possible letters.
- Therefore, for each of the last 3 positions, there are 26 choices.

4. **Calculate the total combinations for the last 3 positions**:
- Since there are 3 positions and each position has 26 options, the total combinations for the last 3 positions is:
\[ 26 \times 26 \times 26 = 26^3 = 17576 \]

5. **Calculate the total number of license plate combinations**:
- To find the total number of unique license plate numbers, we multiply the combinations from the first 3 positions by the combinations from the last 3 positions:
\[ \text{Total combinations} = (10^3) \times (26^3) = 1000 \times 17576 \]
- Performing the multiplication:
\[ 1000 \times 17576 = 17576000 \]

### Final Answer:
The total number of different license plate numbers that can be made is **17,576,000**.