My Math Forum  

Go Back   My Math Forum > College Math Forum > Advanced Statistics

Advanced Statistics Advanced Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
June 21st, 2011, 07:06 PM   #1
 
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?
nates1984 is offline  
 
June 22nd, 2011, 07:19 AM   #2
Math Team
 
Joined: Dec 2006
From: Lexington, MA

Posts: 3,012
Thanks: 256

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]




soroban is offline  
June 22nd, 2011, 02:27 PM   #3
 
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.
nates1984 is offline  
Reply

  My Math Forum > College Math Forum > Advanced Statistics

Tags
combinations, ncr



Search tags for this page
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





Copyright © 2014 My Math Forum. All rights reserved.