
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 21st, 2011, 07:06 PM  #1 
Newbie Joined: Jun 2011 Posts: 2 Thanks: 0  Combinations (nCr)
Context: The problem asks for the probability that you'll get two pairs in a poker hand. I'm going to omit (11C1 * 4C1) as it isn't relevant to my question. Why is this: 13C1 * 4C2 * 12C1 * 4C2 Not equal to this: 13C2 * 4C2 * 4C2 I must be misunderstanding this concept somewhere. It would appear to me that if you're choosing the same amount of cards in 4CX for multiple groups then you MUST select the groups of four together in the same 13CX combination. This is obvious once you browse the Wikipedia page on poker probability. A full house is (13C1 * 4C3 * 12C1 * 4C2), but (13C2 * 4C3 * 4C2) yields a different answer and is incorrect. It's easy enough to do the algebra. Just cancel out factorials and look at what is left in both cases to see how they are (obviously) different from each other. However, conceptually my brain keeps telling me these two things should be equal. So, why aren't they? 
June 22nd, 2011, 07:19 AM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 405  Re: Combinations (nCr) Hello, nates1984! Quote:
[color=beige]. . [/color] [color=beige]. . [/color] [color=beige]. . [/color] [color=beige]. . [/color] [color=beige]. . [/color] [color=beige]. . [/color] [color=beige]. . [/color] [color=beige]. . [/color]  
June 22nd, 2011, 02:27 PM  #3 
Newbie Joined: Jun 2011 Posts: 2 Thanks: 0  Re: Combinations (nCr)
Thanks for the reply. That made everything very clear. I'm also glad to see this forum has latex tags, I'll make sure to use tex if I post any more questions or offer any answers.


Tags 
combinations, ncr 
Search tags for this page 
13c2 math,13c2 combination,combinationsncr latex,what is 4C2,combination of 12c1,12c1 combination,13!c2! ncr formula,13c2 math possibilities,13c2 math combinations
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
How many combinations  ptk  Advanced Statistics  1  July 29th, 2012 12:05 PM 
Complex Combinations Within Combinations Problem?  bugrocket  Advanced Statistics  2  January 23rd, 2011 05:02 PM 
Combinations within combinations possibilities?  aimpro2000  Advanced Statistics  2  September 20th, 2010 02:12 PM 
Possible combinations  ChrisWhewell  Algebra  2  March 4th, 2010 05:51 PM 
combinations  finitehelp  Algebra  9  July 28th, 2009 11:26 AM 