How many possible license plate number combinations are there?

0
171

LAST MODIFIED:

funny license plate

Each state can have 2,176,782,336 different license plate numbers if the plates are six characters in length and all 26 letters and all 10 digits (0-9) can be used. That’s 2 BILLION with a B.

The mathematical formula for six independent spaces with 36 different options (26 letters and 10 numbers) is 36 x 36 x 36 x 36 x 36 x 36 or 36⁶. This is how you get to the 2,176,782,336 number.

Some states have seven character license plates. This means each of those states has a possible 78.4 billion license plate numbers.

Of course, there are exceptions to this.

  1. Some states don’t use O because it looks too much like 0.
  2. No state that I am aware of allows obscene words.
  3. Some states don’t use all ten digits.
  4. Some states use three letters for the first three positions and three digits for the final three positions and vice versa. In this case, the formula would be 26 x 26 x 26 x 10 x 10 x 10, or 26³ x 10³, or (26 x 10)³,  which equals to 17,576,000.

…… and on and on.

INTERESTING FACTS
  1. The first state-issued plate in Massachusetts was issued to Frederick Tudor in 1903 and read, “1.”
  2. In 1931, Pennsylvania was the first state to offer personalized license plates.
  3. There was no standard for license plate sizes until 1957.
  4. In Idaho in 1928, a potato was the first graphic to appear on a license plate.
  5. Today, all but three states use correctional facilities to produce license plates. Alaska, Hawaii, and Oregon are the exceptions.
INTERESTING VIDEO

INTERESTING REFERENCES
  1. ChrystlerCapital.com – 12 LITTLE-KNOWN FACTS ABOUT LICENSE PLATES
  2. MathForum.org – License Plate Combinations
  3. URegina.ca – permutations and combinations
  4. My brain

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