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Math Help - Need formula to calculate # of unique combinations as n & m vary

  1. #1
    a^2
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    Need formula to calculate # of unique combinations as n & m vary

    Can anyone give me a formula to solve the following kind of problem?

    Take n different colors of sand.
    Using a minimum quantity m (i.e. 1%) create all the possible % combinations of the colors. {0, 0, 0, .... 100}, {100, 0, 0, 0, ... 0}, {0, 1, 0, 0, ...99}, etc.

    I need a formula to calculate how many different unique combinations I would get as n and m vary.

    At first I thought I could do this with

    n^(m-1)

    but I'm not so certain now.

    Thx
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  2. #2
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    Please clarify what you mean. I simply cannot understand what you are asking.
    What do {0, 0, 0, .... 100}, {100, 0, 0, 0, ... 0}, {0, 1, 0, 0, ...99}, repesent?
    Do you have 100 colors? Or do you have 100 positions?
    What does m% have to do with the count?
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  3. #3
    a^2
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    Clarification

    I meant the sets {...} to represent all the possible combinations of the different colors of sands, given in the described case, 1% increments. The sets could also include 0% in all but 1 of the colors hence my unclear representation of {0%, 0% ,0%, ... 100%} or any other combination where the total of any given set equals 100%.

    So m would equal the number (in this case) 1% intervals up to and including 100%. Other cases could have different steps or even be continuous.

    So I need a formula to count all the possible combinations given n sand and m intervals.

    I hope this makes it a bit clearer.

    Thx.
    Last edited by a^2; September 22nd 2008 at 04:33 PM. Reason: Clarification
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