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Math Help - Combinations

  1. #1
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    Combinations

    I am trying to work out the number of combination's a particular problem has.


    The problem:

    Lets say there are 3 nodes. Each node is assigned a color, and there are three possible colors each node can be.

    How many combinations are there?


    Is the answer just 3^3?


    Thanks

    Calypso
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  2. #2
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    Quote Originally Posted by calypso View Post
    I am trying to work out the number of combination's a particular problem has.


    The problem:

    Lets say there are 3 nodes. Each node is assigned a color, and there are three possible colors each node can be.

    How many combinations are there?


    Is the answer just 3^3?


    Thanks

    Calypso
    Hi Calypso,

    Yes.

    Suppose the nodes may be red, green or blue.
    Then the combinations may be listed or you could draw a tree diagram

    RRR
    RRG
    RRB

    RGR
    RGG
    RGB

    RBR
    RBG
    RBB

    If the first node is Red, then there are 3(3) combinations.
    We triple this to account for the first node being Green or Blue.
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  3. #3
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    Great thanks for confirming the answer. Just have one further question if you dont mind..

    Lets say now the three nodes are connected together by 3 bars. Each bar has a thickness and there are 10 possible thicknessess.

    Going by the above logic the total number of combinations for bars is 3^10.


    And the total combinations for nodes is 3^3


    So does that mean that the total number of combinations including nodes and bars is

    a ) (3^3) + (3^10)

    b) (3^3) ^ (3^10)

    c) (3^10) ^ (3^3)

    Thanks in advance

    Calypso
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  4. #4
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    After thinking about the problem for a while I think the answer is more lilkely to be

    d) (3^10) * (3^3)

    Is this right?
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  5. #5
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    Quote Originally Posted by calypso View Post
    After thinking about the problem for a while I think the answer is more lilkely to be

    d) (3^10) * (3^3)

    Is this right?
    That's almost it.

    The answer is

    10^3(3^3)

    Taking any one arrangement of node colours...

    The first bar can be any of 10 sizes,
    2nd one can be any of 10 sizes,
    3rd can be any of 10 sizes..

    which is (10)(10)(10) arrangements of bar sizes with the 3 nodes connected
    like a triangle, for any one colour combination.
    Last edited by Archie Meade; April 6th 2010 at 10:15 AM. Reason: misread
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  6. #6
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    Great, Thanks
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