
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 9th, 2016, 10:44 PM  #1 
Senior Member Joined: Apr 2008 Posts: 194 Thanks: 3  a card game in probability
4 cards are dealt from a 52card deck. How many hands contain 2 distinct pairs? This is how I do it. From the 13 ranks, I choose 1. In this rank, I choose 2 cards from 4. From the remaining 12 ranks, I choose 1. In this rank, I choose 2 cards from 4. Now, I do the following calculations. 13C1*4C2*12C1*4C2 = 5616. But the answer key says 2808. If I divide my answer by 2, I will get the right answer. But I don't why I have to do that. Please explain it. Thank you very much. 
May 10th, 2016, 12:51 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
You doublecount each pair because, for example, A + 5 and 5 + A are both counted.

May 10th, 2016, 10:57 AM  #3 
Senior Member Joined: Apr 2008 Posts: 194 Thanks: 3 
In my calculation, I choose 2 cards from 4 in one rank and do the same thing in a different rank. I don't see how doublecounting occurs.

May 11th, 2016, 09:15 PM  #4 
Senior Member Joined: Apr 2008 Posts: 194 Thanks: 3 
I have thought about my solution for some time. Because I am using combinations where the order does not matter, arrangements of the same objects count only once. For example, abc acb bac bca cab cba. There is only one combination of the three letters. I am confused about why I have to divide my answer by two.


Tags 
card, game, probability 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Odds of guessing a playing card value in a new card game  jaketyler27  Probability and Statistics  0  April 17th, 2015 11:58 PM 
Probability of *not* guessing the right card in a 52card deck...  cbenson4  Probability and Statistics  1  March 5th, 2015 11:56 AM 
how to solve this card game probability problem  davedave  Probability and Statistics  7  March 14th, 2012 08:36 AM 
Probability in a Trading Card Game??  RayZorback  Advanced Statistics  3  June 30th, 2008 12:49 PM 
Probability in a Trading Card Game??  RayZorback  Algebra  1  June 18th, 2008 07:48 AM 