A license plate consists of two letters followed by three numerical digits (e.g. MX556).

Question

How many different license plates can be made if no two-character U.S. state abbreviations are allowed for the

two letters?

Answer 1

There are 26 possibilities for the first character (A - Z) and 26 possibilities for the second character (A - Z) which give us 26 x 26 or 676 total possibilities for the two letters. From those, we need to remove the 50 state abbreviations so 676 - 50 = 626.

There are 10 possible numbers for the third character (0 - 9) as well as 10 possible numbers for the fourth and fifth characters meaning there are 10 x 10 x 10 or 1000 total possibilities for the numbers.

The combination of letters and numbers would just be 626 x 1000 or 626,000 different license plates.