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Combinations Question Please Help Urgently!

  1. Apr 5, 2010 #1
    1. The problem statement, all variables and given/known data

    There are a total of 30 members of Parliament in a new country called JanesWorld. Among these deputies, there are 10 from the “Conservative Janes” , 8 from the “Progressive Janes” and 12 independents . How many ways can Queen Jane form a parliamentary committee of 11 parliamentarians, if:
    (a) the committee must contain at least one independent ; (b) the committee must contain at most two independents ; (c) the committee has exactly six Conservative Janes, but the Conservative X and the Progressive Y cannot be on the committee at the same time.

    2. Relevant equations
    Combinations and Permutations

    3. The attempt at a solution

    a) Total number of possible committees= C(30,11)
    # of committees without independents= C(18,11)
    Therefore, numer of committees with atleast one independent= C(30,11)- C(18,11)

    b) Total number of possible commitees= C( 30,11)
    Total # of committes without independents= C(18,11)
    Total # of comm. with 1 independent= C( 12,1) x C( 18,10) ????
    Total number of committees with 2 independents= C( 12,2) x C( 18,9) ????

    c) Choosing 6 out of 10 conservatives= C( 10,6)
    Total number of comittees= C(30,11)= C(10,6)+ C(20,5)
    Possibility of X being in committee= C( 10,1)
    Possiblity of Y being in committee= C( 20,8) x C(8,1) ??????????????
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Apr 6, 2010 #2


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    Science Advisor
    Homework Helper
    Gold Member

    That looks good.

    Yes, so add those three up...

    I'm not sure I understand what (c) is asking for. Is it saying that if there are any conservatives there can be no progressives? If so, wouldn't it just be C(10,6)*C(12,5)?
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