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Hexadecimal numbers are made using the sixteen digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. They are denoted by the subscript 16. For example, 9A2D16 and BC5416 are hexadecimal numbers.
a. How many hexadecimal numbers begin with one of the digits 3 through B, end with one of the digits 5 through F, and are 5 digits long?
b. How many hexadecimal numbers begin with one of the digits 4 through D, end with one of the digits 2 through E, and are 6 digits long?

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LammettHash

a. There are 9 choices of first digit taken from the range 3-B; there are 11 choices for the last digit in the range 5-F; and there are 16 choices of digit for the remaining 3 positions. This means there are

9 × 16³ × 11 = 405,504

such hexadecimal numbers.

b. There are 10 choices for the first digit (4-D), 13 choices for the last digit, and 16 for the other 4 positions. So there are

10 × 16⁴ × 13 = 8,519,680

such hexadecimal numbers.

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