Motorcycle plates in colorado have three numbers followed by three letters. how many motorcycle plates area available with these restrictions? (assume there are no other restrictions.)

When you have a counting problem like this, you have to think in terms of how many choices you have. A generic plate is like this:

so, you have 10 choices for each of the first three places, and 26 choices for each of the last three places.

This leads to a total of

possible plates.