How many cars can have a license plate without repeating?

Answer 1

You need to specify the license plate format.

In many states, the fomat is "three letters, three digits" (or the other way around; I can't remember which is which, but Massachusetts and New Hampshire do them exactly backward from each other).

This gives 26x26x26x10x10x10 possible combinations: a bit over 17 and a half million unique plates.

Some of these may have unfortunate letter combinations. Most states won't give out license plates with SEX or SIN or the like (in fact, a lot of them don't use either I or O at all, because of the possibility of confusion with 1 and 0). Leaving out I, O, and "objectionable" letter combinations drops it to roughly 13 million unique plates.

In most states this is more than sufficient for every single vehicle in the state to have at least one plate. The most populous states (California, Texas, New York, and Florida) have more than 13 million residents each, though, so even though children under 16 probably don't need license plates, it's possible that between commercial vehicles (which often use a different scheme anyway that doesn't overlap with passenger cars) and some people owning more than one vehicle, they might run up against that limit either now or in the near future.

California handles it by adding another digit, bumping the number of unique plates up to 130 million, which should last a while. I'm honestly not sure how the other states manage ... they may abandon the letter/digit pattern and allow any position to have either a letter or a digit, thus giving 34^6 (over 1.5 billion) possibilities.