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Bags of marbles combination/permutation problem

  1. Dec 16, 2007 #1
    Okie. Here goes...

    Let's say you have B bags of marbles B1, B2,...Bb (all marbles are unique);
    The number of marbles in each bag varies. B1 has n1 marbles, B2 has n2 marbles, etc.

    You want to to create a sequences of B marbles
    {marble1, marble2,....marbleb}, where marble1 came from B1, marble2 from B2, etc.

    The total number of permutations is n1*n2*....nb.

    But...suppose you now only allow m marbles in each permutation to be duplicated.

    //////////////////Question:How many permutations are there now?//////////////////////



    Ex: You have 3 bags of marbles.
    B1 {red,green,blue}, n1 = 3;
    B2 {white,black}, n2 = 2;
    B3 {silver,gold}, n3 = 2;

    I will only allow 1 marble to be duplicated, so

    {red,white,silver}
    {red,black,gold}
    {green,white,gold}
    {green,black,silver}

    Can't use blue now because the options would be...
    {blue,white,gold}// { x, white, gold} was used in {green,white,gold} so would have 2 duplicated marbles
    {blue,white,silver}// { x, white, silver} was used in {red,white,silver} so would have 2 duplicated marbles
    {blue,black,gold}// { x, black,gold} was used in {red,black,gold} so would have 2 duplicated marbles
    {blue,black,silver}// { x, black, silver} was used in {green,black,silver} so would have 2 duplicated marbles



    Any help would be appreciated.

    Thx! :)
     
    Last edited: Dec 16, 2007
  2. jcsd
  3. Dec 22, 2007 #2
    Try to figure it out for your small example and then generalize it for your homework problem.
     
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