A state's license plate contains 3 letters followed by 3 digits. How many different license plates are possible? Explain your answer.

YOu don't specify if repetitions are allowed, but I will assume we can repeat letters and digits.

so number of ways = 26x26x26x10x10x10 = ...

To find the number of different license plates that are possible in this scenario, we need to determine the total number of choices for each individual component (letters and digits) and then multiply those choices together.

1. For the first letter on the license plate, there are 26 choices (26 letters in the English alphabet).
2. For the second letter, we have the same 26 choices available since repetition is allowed.
3. For the third letter, again, we have 26 choices.
4. For the first digit, there are 10 choices (digits 0-9).
5. For the second digit, we have the same 10 choices available.
6. Finally, for the third digit, we also have 10 choices.

To find the total number of possible license plates, we multiply the number of choices for each component together:

26 * 26 * 26 * 10 * 10 * 10 = 17,576,000

Therefore, there are 17,576,000 different possible license plates in this scenario.

To find the number of different license plates possible, we need to multiply the number of possibilities for each component of the license plate.

1. Letters:
Since there are 26 letters in the English alphabet, and we need 3 letters for the license plate, there are 26 options for the first letter, 26 options for the second letter, and 26 options for the third letter. Multiplying these together, we get 26 x 26 x 26 = 17,576 possible combinations for the letters.

2. Digits:
Since there are 10 digits (0-9), and we need 3 digits for the license plate, there are 10 options for the first digit, 10 options for the second digit, and 10 options for the third digit. Multiplying these together, we get 10 x 10 x 10 = 1,000 possible combinations for the digits.

3. Combining the possibilities:
To find the total number of license plates possible, we multiply the number of letter combinations by the number of digit combinations: 17,576 x 1,000 = 17,576,000.

Therefore, there are 17,576,000 different license plates possible with 3 letters followed by 3 digits.

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