My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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?
Majestic_Q is offline  
 
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 12-k 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
brunojo is offline  
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
Majestic_Q is offline  
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
Majestic_Q is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
boys, dividing, girls, probability, question



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Boys and some Sweets puzzle Puzzled16 Algebra 13 March 6th, 2014 04:05 PM
Probability of Choosing Boys & Girls Abstract3000 Probability and Statistics 5 February 25th, 2014 08:34 PM
Dividing by zero Chikis Elementary Math 4 March 12th, 2013 09:03 AM
Dividing by zero? Jo15 Calculus 7 January 1st, 2012 07:51 PM
ten boys can rob 30 warqzaka Algebra 4 July 5th, 2011 10:06 AM





Copyright © 2017 My Math Forum. All rights reserved.