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Is the number randomly generated? If not, then I think the probability is wrong since there are many series of numbers that have never been issued

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The numbers are generated in order. They started with 0000-BBB, then 0001-BBB, and it'll continue until 9999-ZZZ. We're currently around MDB. This means that it's a good approximation to assume all the numbers are equally probable.

Ah ok, wasn't sure if the numbers incremented first or the letters

this would be much easier in a state that was AAA-#### as there'd be a much more even distribution of numbers

California is relatively close with #AAA###, I remember using spotting new first # as an indicator as to how many cars had been bought.

Yep, my parents purchased a car in 1978 that was still on "NNN AAA". Then our next car was a 1986 model, and I believe it was a "1 AAA NNN" series. By 1993, I purchased a car with ridiculous vanity plates, so I immediately pulled them off and registered normally, receiving a "3" series plate.

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