To determine the total number of possible license plates, we can break the problem into two parts: calculating the number of choices for letters and the number of choices for digits.

Step 1: Finding the Number of Choices for Letters

Each license plate has 3 letters, and the letters H and L are not used. That means we are left with $26 - 2 = 24$ letters.

Since letters can be repeated, the total number of possibilities for the 3-letter combination is: $24 \times 24 \times 24 = 24^3$

Step 2: Finding the Number of Choices for Digits

Each license plate also has 3 digits, and the digits 1, 2, and 9 are not used. That leaves $10 - 3 = 7$ digits.

With repetition allowed, the total number of possibilities for the 3-digit combination is: $7 \times 7 \times 7 = 7^3$

Step 3: Combining Letters and Digits

To find the total number of license plates, multiply the number of possibilities for the letters and digits: $24^3 \times 7^3$

Calculating each value separately: $24^3 = 24 \times 24 \times 24 = 13,824$ $7^3 = 7 \times 7 \times 7 = 343$

Now, multiply these two results: $13,824 \times 343 = 4,742,832$

Final Answer

The total number of license plates that can be generated is: $\boxed{4,742,832}$

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Would you like more details, or have any questions?

Related Questions

1. How would the solution change if repetition of letters was not allowed?
2. What if each plate had 4 letters followed by 2 digits instead?
3. How many license plates can be formed if only vowels were excluded from the letters?
4. What if the format was 2 letters followed by 4 digits?
5. What is the probability of generating a plate with the same letter repeated three times?

Tip:

When dealing with repetition problems, count the number of possibilities for each position and multiply them together.