Problem 2030. A Poker Hand

Created by Khizar

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Texas Hold ‘Em is a classical card game. In this problem, we are concerned with determining the probability of attaining a certain type of hand.

A “Full House” is a five card hand comprised composed of two sets: a set of three of a kind, and a set of two of a kind. Examples include: K-K-K-Q-Q, 10-10-10-5-5, and A-A-A-4-4.

Assuming that there are 52 cards in a unique, distinguishable deck, find the probability of attaining a “Full House” in any given hand. You may assume that there are 9 players playing on a full table.

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Last Solution submitted on Jun 08, 2025

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3 Comments

Alfonso Nieto-Castanon on 2 Dec 2013

I believe the probability is 10 times what you say it is (if in % units) or 1/10th of what you say (if in /1 units)

James on 4 Dec 2013

Agreed. I got the same result: off by a factor of 10 in one direction or the other.

Rafael S.T. Vieira on 25 Sep 2020

I've got the same result as James and Alfonso using a different method. New solvers must multiply the solution by 10 until the problem is fixed (if it is ever since it has been already 7 years from the time the issue was first seen).

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Problem 2030. A Poker Hand

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Problem 2030. A Poker Hand

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Last 200 Solutions

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Problem Recent Solvers30

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