Combinations of poker hands

In summary, the conversation discusses the number of different hands that can be dealt in a variant of Poker, where each player is dealt a hand of 6 cards from a standard pack. The specific type of hand being considered is three pairs, which consists of two cards of the same value, another 2 of a different value, and a third pair of a third value. The solution proposed by one participant is to start with 13C3 (the number of ways of choosing 3 cards out of 13) and then add 12C3, 11C3, etc. However, another participant suggests taking a more systematic approach by considering the number of different numbers (3) and the number of cards for each number (2
  • #1
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In a varient of Poker each player is dealt a hand of 6 cards from a standard pack How many hands are there of each of the following types?

Three pairs: Two cards of the same value. another 2 of a differnt value, and a 3rd paid of a third value. i.e Q(clubs) Q(diamonds) 6(hearts) 6(diamonds) 4(spades) 4(hearts)

..

For my attempt I started with 13C3 + 12C3 +11C3 ... + 3C3 = 1001 different hands

But this hasn't accounted for the differnt variation of suits, threre are 6 possible pairs of suits, so i multiply 1001 by 6?

thanks for any help!
 
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  • #2
noone? :(
 
  • #3
Hi Firepanda! :smile:

Firepanda said:
For my attempt I started with 13C3 + 12C3 +11C3 ... + 3C3 = 1001 different hands

erm … 13C3 is the number of ways of choosing 3 cards out of 13 … but what did you think was the reason for adding 12C3 etc?

Be systematic. One step at a time.

First step: there have to be three different numbers (eg 2 5 Q).

Second step: for each number, there have to be 2 cards of that number.

Try it that way! :smile:
 

1. What is a combination of poker hands?

A combination of poker hands is a set of five cards that make up a player’s hand in a game of poker. These cards can be a mix of face-up cards on the table and hidden cards in a player’s hand.

2. How many different combinations of poker hands are there?

There are 2,598,960 possible combinations of poker hands in a standard 52-card deck. This includes different combinations of cards with different suits and ranks.

3. What is the best combination of poker hands?

The best combination of poker hands is a royal flush, which consists of a 10, Jack, Queen, King, and Ace of the same suit. This is the highest-ranking hand in poker and is very difficult to obtain.

4. What is the probability of getting a specific combination of poker hands?

The probability of getting a specific combination of poker hands varies depending on the hand. For example, the probability of getting a royal flush is 1 in 649,739, while the probability of getting a pair is 1 in 2.37.

5. Can the combination of poker hands change during a game?

Yes, the combination of poker hands can change during a game as new cards are dealt or players choose to exchange cards. This is why poker is a game of skill and strategy, as players can try to improve their hand throughout the game.

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