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 can be made.

Explanation:

The order of the digits and of the letters is important. For example, ABC is a different configuration than CBA. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

`P_((n,x)) = (n!)/((n-x)!)`

In this question:

3 digits from a set of 10(there are 10 digits from 0 to 9).

3 letters from a set of 26. So

Total:

`T = P_((10,3)) * P_((26,3)) = (10!)/((10-3)!) * (26!)/((26-3)!) = 11232000`

11232000 plates can be made.