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August 6th, 2010, 04:29 AM  #1 
Newbie Joined: Aug 2010 Posts: 1 Thanks: 0  Card game Combinatorics
Here is a question for you guys.We argued a lot with friends and I a hope to get a clear answer with a proof in here. We have 32 cards and 4 players.All players are dealt 5 cards the first round so there are 12 cards left on the stack that will be dealt with 3 cards to each player.The question is: If one of the players has three of a kind(kings), what is the probability that he gets the fourth king in the second round when the last 12 cards are dealt. So one more time: 32 cards overall.Every player gets 5 cards the first round.One of them has a three of a kind (kings).What is the probability that he will get the fourth one when the last 12 cards are dealt between the four players(each one receives three and we assume the fourth king is among these last 12 cards).thank you guys I hope you have fun with this question and pls give a proof for the answer 
August 6th, 2010, 12:46 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,709 Thanks: 675  Re: Card game Combinatorics
Under the assumption that the king is among the last 12 cards, he has probability of 1/4 to get it. The simplest way to look at is each player has the same chance (1/4) of getting the king. The problem gets more interesting when you drop the assumption that the king is among the 12. Then the probability it will be among the 12 is 12/27, so the probability that the player with the 3 kings gets the fourth king is 3/27 = 1/9. 

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