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December 17th, 2008, 10:32 AM  #1 
Newbie Joined: Sep 2008 Posts: 9 Thanks: 0  Probability Question  12 girls and 10 boys dividing into...
Need help desperately: In the class there are 10 boys and 12 girls The students randomly divide into pairs, what's the probability they'll divide into 10 mixed pairs (1 boy and 1 girl) with 1 pair of 2 girls? I've been going crazy over this...I've tried to do 11!x2!x2!x2!x2!x2!x2!x2!x2!x2!x2!x2! but I don't think it's the right answer. What am I missing? Help, please? 
December 17th, 2008, 12:47 PM  #2 
Senior Member Joined: Nov 2007 Posts: 258 Thanks: 0  Re: Probability Question  12 girls and 10 boys dividing into...
You probably know that which generalizes easily to unions of more than two sets. Here if are the events "Boy j pairs up with a girl" we have (because after k boys have hoooked up, there are 2k people out and 12k girls remaining) Hope that helps! Nice problem, it's not obvious that the probability is 1/2 at every pick. Although I'm sure in real life it's a bit bigger 
December 21st, 2008, 10:17 AM  #3 
Newbie Joined: Sep 2008 Posts: 9 Thanks: 0  Re: Probability Question  12 girls and 10 boys dividing into...
Thank you, helped me understand 
December 21st, 2008, 12:46 PM  #4 
Newbie Joined: Sep 2008 Posts: 9 Thanks: 0  Re: Probability Question  12 girls and 10 boys dividing into...
Okay, that's what I came up with: 12/22*10/21*11/20*9/19*10/18*8/17*9/16*7/15*8/14*6/13*7/12*5/11*6/10*4/9*5/8*3/7*4/6*2/5*3/4*1/3*2/2*1/1 = 1/646646 2!*2!*2!*2!*2!*2!*2!*2!*2!*2!*2!=2048 1/646646*2048= 2048/323323*100 = 0.6334% Hope I'm right 

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boys, dividing, girls, probability, question 
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