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How many distinct 3 digit odd integers are there? Distinct meaning none of the digits repeat.

  • math -

    first digit: 9 choices (1-9)
    then, 2nd digit: 9 choices (now 0 is allowed)
    then, 3rd digit: 8 choices

    so, 9*9*8

  • math -

    It has to be odd, so the 3rd digit has to be 1, 3, 5, 7, or 9. So there are only 5 options. Moreover, you do not consider the cases in which the digits do not repeat.

  • math -

    you got me on the odd value, but I do account for the non-repeatability of digits.

    If they can be repeated, then there would be 9*10*10 possibilities for 3 digits.
    My counting forces the preceding choices not to be used again.

    Since the number must be odd, things get a bit more complicated, because we don't know whether the previous choices were odd or even.

    You seem to have a handle on the problem. What is your reasoning?

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