If a state wants each of its license plates to contain 3 different letters of the alphabet followed by 5 different digits, how many different license plates can it make

There are 26 alphabets, and we want the first 3 to be different alphabets. So, the first three characters have the probability:

Next, we want 5 different digits. There are 10 total digits (including 0), so that will look like:

Combining those two statements, we get:

Thus, your answer is 471744000.