Question

Standard issue passenger license plates in Ohio consist of three letters followed by four numbers. How many standard issue license plates can be produced if there are no restrictions on the letters and numbers?

Answer 1

The standard issue license plates that can be produced if there are no restrictions on the letters and numbers = 175760000

Explanation:

If there are no restrictions, all numbers and letters are available to be used then. And with no restrictions, every number or letter can appear more than once.

There are 7 spaces available; 3 spaces for letters, 4 spaces for numbers

The different combination of letters and numbers then becomes,

26 × 26 × 26 × 10 × 10 × 10 × 10

This is because, all 26 letters (A to Z) can occupy the first space, the second space and the third space. And all 10 digits (0 to 9) can occupy the fourth space, the fifth space, the sixth space and the seventh space.

So, the standard issue license plates that can be produced if there are no restrictions on the letters and numbers = 26 × 26 × 26 × 10 × 10 × 10 × 10 = 175760000 different standard issue license plates.