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The problem asks how many different license plates can be created, where each license plate contains 3 letters (from the 26 letters in the alphabet) followed by 2 digits (from 0 to 9). The condition is that no letters or digits are repeated.

Let's break it down step by step:

1. **Choosing the letters**:
   - There are 26 possible letters for the first position.
   - For the second position, we can only choose from the remaining 25 letters (no repeats).
   - For the third position, we can only choose from the remaining 24 letters.

   So, the total number of ways to choose the letters is:
   \[
   26 \times 25 \times 24
   \]

2. **Choosing the digits**:
   - There are 10 possible digits for the first position (digits 0-9).
   - For the second position, we can only choose from the remaining 9 digits (no repeats).

   So, the total number of ways to choose the digits is:
   \[
   10 \times 9
   \]

3. **Multiplying these together**:
   The total number of possible license plates is:
   \[
   (26 \times 25 \times 24) \times (10 \times 9)
   \]

Let's compute this:
\[
26 \times 25 \times 24 = 15600
\]
\[
10 \times 9 = 90
\]
\[
15600 \times 90 = 1,404,000
\]

Thus, there are **1,404,000** different possible license plates.

Let me know if you have any questions or need more details!

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Here are 5 related questions for further practice:
1. What if the license plates allowed repeated letters but not repeated digits?
2. How many license plates can be formed if both letters and digits can be repeated?
3. What if the license plate required 4 letters and 3 digits with no repeats?
4. How would the number of license plates change if only certain letters (like vowels) could be used?
5. How would the result change if the digits were allowed to be repeated but the letters were not?

**Tip**: For problems like this, breaking down the choices into separate steps (like letters and digits) and considering restrictions (like no repeats) makes the process manageable.

How many different license plates are possible if each contains 3 letters (out of the alphabet's 26 letters) followed by 2 digits (from 0 to 9)? How many of these license plates have no repeated letters and no repeated digits?

Discover how to calculate the total number of unique license plates possible using 3 letters and 2 digits with no repetitions. This combinatorics problem explores permutations without repetition and is perfect for students in Grades 9-12.

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