Question

Tags in Delaware consist of two letters followed by three numbers. If the letters can be repeated but the numbers cannot be repeated, how many possible different car tags can be generated?

Answer 1

We have 26 letters and 10 digits.

So, we have 26 choices for the first letter, 25 choices for the second letter (we can't pick the one we already chose), and 10 choices per digit (we can always choose any digit, because we can repeat them).

This leads to a total of

$26\cdot25\cdot10\cdot10\cdot10=650000$

possible car targs.