Hello, lhurlbert!
I don't see the resoning behind your answer/
How many license plates contain at most 3 numerals followed by exactly 4 distinct letters?
It starts with at most 3 digits.
It can have no digits: 1 way.
It can have any number from 1 to 999.
. . Hence, there are 1000 choices for the numerals.
. .
As you can see the answer above differs from the one I gave.
Here is why: I read the question in such a way that the plates are different.
In other words: There is 1 way for no digits.
There are 10 ways for one digit.
There are 100 ways for two digits.
There are 1000 ways for three digits.