
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 26th, 2018, 04:26 PM  #1 
Member Joined: Oct 2017 From: Rumba Posts: 34 Thanks: 0  Discrete Math question Any ideas how to do this? Thanks Last edited by sita; February 26th, 2018 at 04:29 PM. 
February 26th, 2018, 04:58 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,202 Thanks: 1156 
I don't know about the hint, but $\dbinom{2n}{2} = \dfrac{(2n)!}{2!(2n2)!} = \dfrac{(2n)(2n1)}{2} = n(2n1)$ $2\dbinom{n}{2} = 2\dfrac{n!}{2(n2)!} =n(n1)$ $\dbinom{2n}{2}2\dbinom{n}{2} = 2n^2  n  (n^2n) = (2n^2n^2)(nn) = n^2$ $n^2 + 2 \dbinom{n}{2} = \dbinom{2n}{2}$ 
February 26th, 2018, 10:06 PM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,202 Thanks: 1156 
What the hint is referring to is the idea of splitting the $2n$ items into 2 mutually exclusive sets of $n$ each. Each of these two subsets has $\dbinom{n}{2}$ ways of selecting 2 items from them. This is the $2\dbinom{n}{2}$ term. Then you can pair up 1 item from each subset. These will be distinct from any of the pairs chosen entirely from one of the subsets. There are $n^2$ pairs you can make. The sum of these two terms account for all the pairs you can make from the original $2n$ items. 
February 27th, 2018, 04:06 AM  #4 
Senior Member Joined: Feb 2010 Posts: 697 Thanks: 135  Maybe a story something like this. In how many ways can you choose $\displaystyle 2$ people from a group of $\displaystyle n$ boys and $\displaystyle n$ girls? You can either choose one of each gender $\displaystyle n \times n = n^2$ or you can choose both the same gender $\displaystyle 2 \binom{n}{2}$ (multiply by two since there are two genders). 

Tags 
discrete, math, question 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Question Discrete Math Binomial Theorem  sita  Probability and Statistics  2  February 17th, 2018 12:48 PM 
Discrete Math question  sita  Probability and Statistics  1  February 10th, 2018 06:44 PM 
Discrete math direct proof question  mgk501  Real Analysis  2  March 21st, 2013 01:23 PM 
Discrete math set question someone help?? thank you  peiyilee  Applied Math  0  March 24th, 2008 09:46 AM 