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There are 264 = 456,976 permutations of 4 letters of the Roman alphabet.

There are 103 = 1,000 permutations of 3 digits of the Roman alphabet.

These letters and digits can be ordered in 7C3 = 7*6*5/(3*2*1) = 35 ways.

So all in all, there are 456,976*1,000*35 = 15,994,160,000 possibilities.

However:

  • letters that may be confused with numbers (O, I, Q, Z) are usually excluded. Excluding only 4 letters almost halves the first of the above number [224 = 234,256].
  • letter combinations that form (or are suggestive of) words considered obscene are usually not issued. Effect unknown.
  • characters in license plates are usually grouped: for example the UK used LLL999Y and then Y999LLL until 2000). This reduces the final factor from 35 to 1.
  • finally, some of the letters or numbers may be used for other purposes, for example to identify the year of issue, of the location. In the UK example, above, Y was used to identify the age when the license was first issued. A set of LLLs were used to identify the location. There was not, therefore, free choice in the characters or numbers.
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