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Combnatorics - selecting out of a group of 13 people

  1. Nov 11, 2009 #1
    out of a group of 5 girls and 8 boys i want to pick a band, for the drums guitar and keyboard i want boys and for the singer and a dancer i want girls.

    how many different ways could i chose the band if there is a boy and a girl who wont be on the band together?

    what i did was find the total amount of ways i can form my band
    5P2*8P3=(5*4)*(8*7*6)=6720

    now i want to subtract the options where those 2 ARE together
    since i NEED those 2 to be in the band i can only choose 1 girl and 2 boys
    ((1*4)*2!)*(1*7*6)*3!)=2016

    (2! and 3! since there are 2! options to organise the 2 girls and 3! for the 3 boys


    6720-2016=4704

    but this is wrong, the answer is 5712, whichis 6720-1008(wich is exactly half of the 2016 that i got)
     
  2. jcsd
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