A state's license plate starts with a digit other than 0 followed by five capital letters (A through Z) followed by one digit (0 through 9) how many different license plates are possible?

To determine the number of different license plates possible under the given conditions, we'll calculate the possibilities for each part of the license plate separately and then multiply them together.

### License Plate Structure:
1. **First position**: A digit other than 0 (i.e., 1-9).
2. **Next five positions**: Capital letters (A-Z).
3. **Final position**: Any digit (0-9).

### Step 1: First position (Digit other than 0)
- There are 9 possible choices (1 through 9).

### Step 2: Next five positions (Capital letters)
- For each of the five positions, there are 26 possible letters (A through Z).
- Therefore, for five letters, the total number of possibilities is \(26^5\).

### Step 3: Final position (Any digit)
- There are 10 possible choices (0 through 9).

### Final Calculation
To find the total number of possible license plates, multiply the possibilities for each part:

\[
9 \times 26^5 \times 10
\]

Now let's calculate it:

\[
26^5 = 26 \times 26 \times 26 \times 26 \times 26 = 11,881,376
\]
\[
9 \times 11,881,376 \times 10 = 1,069,323,840
\]

Thus, the total number of different license plates possible is **1,069,323,840**.

Would you like a detailed breakdown or have any further questions?

### Expanding the Information:
1. How would the total number of license plates change if the first digit could also be 0?
2. What if lowercase letters were also allowed in the five-letter sequence?
3. How many license plates would be possible if two digits were added to the end?
4. How would the number of possibilities change if all letters could repeat?
5. What is the probability of randomly generating a specific license plate?

### Tip:
When solving combinatorial problems, breaking down each section and multiplying the outcomes for each possibility ensures accurate results.

Discover how to calculate the total number of different license plates possible, with the first digit being between 1-9, followed by five capital letters, and ending with any digit (0-9). The solution uses combinatorial mathematics and the multiplication principle for a final result of 1,069,323,840 possible combinations.

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