How many different license plates can be made if each plate contains a sequence of three uppercase English letters followed by three digits?

To determine how many different license plates can be made if each plate contains a sequence of three uppercase English letters followed by three digits, we can break down the problem into two parts:

1. **Letters**: There are 26 uppercase English letters, and the plate contains a sequence of three letters.
   - The number of possible combinations for the letters is \( 26 \times 26 \times 26 = 26^3 \).

2. **Digits**: There are 10 digits (0 through 9), and the plate contains a sequence of three digits.
   - The number of possible combinations for the digits is \( 10 \times 10 \times 10 = 10^3 \).

Now, to find the total number of possible license plates, multiply the number of combinations for the letters by the number of combinations for the digits:

\[
26^3 \times 10^3 = 17,576 \times 1,000 = 17,576,000
\]

Thus, there are **17,576,000** different possible license plates.

Would you like more details or have any questions?

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Here are 5 related questions to explore further:

1. How many different license plates can be made if the plate contains four letters followed by two digits?
2. What if the license plate contained two letters followed by four digits?
3. How would the total number of license plates change if lowercase letters were allowed?
4. How many license plates can be made if repetition of letters or digits is not allowed?
5. How many license plates can be made if the sequence of letters and digits can be in any order?

**Tip:** Understanding combinatorics can help in calculating permutations and combinations for various scenarios.

Discover how to calculate the total number of possible license plates with a combination of 3 uppercase English letters and 3 digits. This problem explores combinatorics and the counting principle, suitable for students in Grades 8-10.

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