Anonymous asked in Science & MathematicsMathematics · 9 years ago

How many numbers from the set {1,2,...,9999} use exactly two different digits?

For example: 1121 should be counted, but 3333 and 1231 should not.


2 Answers

  • 9 years ago
    Best Answer

    count all occurences of each:

    9 possibilities for a, (1-9)

    9 possibilities for b, (0-9) minus whatever a is.

    ab: 9*9 = 81 possibilities. The same goes for each of the following:

    aab, aba, abb, aaab, aaba, aabb, abaa, abab, abba, abbb

    Total = 11 configurations * 81 possibilities = 891 possible number configurations.

    Note: you would NOT also consider ba, baa, bab, bba, etc.

    a just represents whatever the first digit is, and it can be 1-9, it's not like b being 1-9 would be any different, so doubling it would give you an incorrect result.

  • M
    Lv 5
    9 years ago

    Do your own homework.

    Oops :P

    But seriously, you Only learn by doing.

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