Suppose a license plate contains two DISTINCT letters follow

Suppose a license plate contains two DISTINCT letters followed by three digits with the first digit not zero. How many different license plates be printed?

Solution

There are 26 letters for the first letter, and 25 letters for the second letter.

There are 9 numbers for the first digit (0 is not allowed), and 10 digits for the second and third digits.

Thus, there are 26*25*9*10*10 = 585000 license plates. [ANSWER]