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Given a four digit number XXXX, are there more permutations if repetition is allowed or not allowed?

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Anonymous

  1. with no repetitions, there are only 4! permutations.
    With repetition, there are 10^4 (or maybe 9*10^3 if you disallow leading zeros) choices.

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    Steve

  2. if a zero is allowed in the lead position, then with no repetition, there would be
    10(9)(8)(7) ways
    if a zero is allowed in the lead position, and repetition is allowed, there would be
    10^4 ways

    If zero is not allowed, with no repetition: 9(9)(8)(7)
    zero not allowed, but with repetition: 9(10^3)

    If XXXX is a specified number, and the numbers are all different,
    then 4! , as Steve said in his first answer

    If XXXX is a specified number and some of the numbers are duplicates, then more
    information is needed.

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    Reiny

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