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Math Help - List of Combinations

  1. #1
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    List of Combinations

    A generic combination = {A,B,C,D,E}, where each capital letter takes on one of the values from its set.

    A = {a1,a2,a3}
    B = {b1,b2}
    C = {c1,c2,c3}
    D = {d1,d2,d3}
    E = {e1,e2,e3,e4}

    An example of a possible combination would be combination(x) = {a1,b2,c2,d1,e4}.

    How many combinations are there? How can I generate a list with all of the combinations? Or, best, can you generate the list and attach it?

    I took my real-world problem and abstracted it to its fundamentals hoping that it would make it possible for one of you to solve the underlying logic.

    Any help very much appreciated. I didn't take any courses in this type of math and unfortunately I don't have anyone I can run this by for help. Thanks!
    Last edited by Will57; October 10th 2011 at 09:09 PM. Reason: more clear
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  2. #2
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    Re: List of Combinations

    Quote Originally Posted by Will57 View Post
    How many combinations are there?
    On this question, I was thinking that I may be able to figure the number of combinations one stage at a time like this (((((E & D) & C)& B) &A)?

    Something like what is explained here: Combination -- from Wolfram MathWorld

    What I really need is the full list of combinations, and I'll be happy to clarify if asked.
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  3. #3
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    Re: List of Combinations

    Quote Originally Posted by Will57 View Post
    A generic combination = {A,B,C,D,E}, where each capital letter takes on one of the values from its set.
    A = {a1,a2,a3}
    B = {b1,b2}
    C = {c1,c2,c3}
    D = {d1,d2,d3}
    E = {e1,e2,e3,e4}
    An example of a possible combination would be combination(x) = {a1,b2,c2,d1,e4}. How many combinations are there?
    The difficulty with such a problem is in its meaning.
    As I read it, we take one from each set.
    In this example there are 3\cdot 2\cdot 3\cdot 3\cdot 4=216 possible selections.

    Do you see how to count the selections?
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  4. #4
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    Re: List of Combinations

    Great! That was my first thought but I was second guessing myself. You've interpreted it correctly, it's just the total number of possible combinations.

    I should be able to build out the 216 in Excel in about 15 mins.

    How could I go about generating a list of the combinations the next time that this comes up when there are more results (i.e. >20,000 combinations)?

    I'm thinking of dusting off Mathematica to see if there is a function that will do that for me, since that program doesn't object to large calculations (even if it can lock up the computer for a few minutes).

    It's always nice when the problem turns out to be easier than I had imagined! Thanks for the help, William.
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