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Assuming that there are 6 alpha-numeric characters with a choice of 1 through 6 characters, the number of combinations possible is 37 to the 6th power, minus 1 or (37^6)-1 making 2,565,726,408 possible combinations.

The number 37 comes from 26 letters in the English alphabet plus 10 numbers plus a blank (for vanity plates). The power of 6 is used for each character place. We subtract 1 because the license plate cannot be completely blank.

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