Question

The standard configuration for an Arizona license plate is 3 digits (0 - 9) followed by 3 letters (of 26). If you can not repeat digits or letters, how many plates (NO COMMAS NEEDED) can be made?

Answer 1

11232000 plates

Explanation:

To find the number of plates that can be made, we just need to check for each space filled how many possible values it can take:

We have 3 digits that can not repeat, so the first digit has 10 possible values (all digits from 0 to 9), the second digit has 9 possible values (as one is already taken) and the third digit has 8 possible values.

For the letters, the first one has 26 possible values, the second one has 25 and the third one has 24.

So the number of different plates is the product of all these possibilities for each digit and letter:

10 * 9 * 8 * 26 * 25 * 24 = 11232000 plates