The question asks how many different car number plates can be produced with three letters followed by three numbers.

Explanation:

1. Three Letters:

   • There are 26 letters in the English alphabet (A to Z).
   • Each letter in the plate can be chosen independently.
   • Therefore, the total number of combinations for the three letters is: $26 \times 26 \times 26 = 26^3$

2. Three Numbers:

   • There are 10 possible digits (0 to 9).
   • Each number can be chosen independently.
   • The total number of combinations for the three numbers is: $10 \times 10 \times 10 = 10^3$

3. Total Combinations:

   • The total number of car number plates is the product of the combinations of letters and numbers: $\text{Total combinations} = 26^3 \times 10^3$

Calculation:

$26^3 = 26 \times 26 \times 26 = 17,576$ $10^3 = 10 \times 10 \times 10 = 1,000$ $\text{Total combinations} = 17,576 \times 1,000 = 17,576,000$

Final Answer:

There are 17,576,000 different car number plates that can be produced.

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Related Questions:

1. What happens to the number of plates if we allow repetition of letters?
2. What if numbers and letters can be placed in any order on the plate?
3. How does the total change if only uppercase letters are allowed?
4. What is the probability of randomly generating a specific plate like "ABC123"?
5. How would the count differ if a plate could include special characters?

Tip:

When solving counting problems, always break the problem into smaller, independent cases (e.g., letters and numbers in this case) and multiply the outcomes of each.