If the license plate has 3 letters followed by 3 digits, the number of possibilities is 26 x 26 x 26 x 10 x 10 x 10 = 17,576,000, but if it is 3 letters and 3 digits in any order you multiply by 6! = 720 so the total now exceeds 12,000,000,000. Throw in more letters and number positions...they can go on for centuries until they duplicate a plate number. [My NY plate has 3 letters followed by 4 digits--I think they can get up to 8 positions and maintain readability.]
But with vanity plates, they could have 8 letters (no digits)...but certain letter combinations have been restricted (=censored).