How to find the number of all possible seven-character format license plates?

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How can I get the total number of 7-character format license plates (capital letter or digit) if:


a) There are no further restrictions:

Number of Capital letters = 26 (A-Z)

Number of Digits = 10 (0-9)

36×35×34×33×32×31×30 = 42072307200


b) If the first 3 characters are letters and the last 4 are numbers:

26×25×24×10×9×8×7 = 78624000


c) If letters and numbers alternate, for example A3B5A7Q or 0Z3Q4Q9:

  • Number of permutations that start with a number:

    10×26×9×25×8×24×7 = 78624000


  • Number of permutations that start with a letter:

    26×10×25×9×24×8×23 = 258336000


  • Total number of permutations:

    78624000 + 258336000 = 336960000



What can be wrong with this approach?