In poker, a player is dealt seven cards and must make the best possible hand out of those cards. The number of ways that this can be done is called the “number of combinations” and is denoted with a big c. For example, the number of ways to choose three cards out of a deck of 52 is
C(52,3) = 52! / (3! * 49!) = 2,600,000
This is because there are 52! ways to arrange all 52 cards in a row, but we don’t care about the order of the three cards we’ve chosen. So we divide by 3! to account for the fact that there are three ways to choose the first card, three ways to choose the second card, and three ways to choose the third card.
And then we divide by 49! because once we’ve chosen our three cards, there are only 49 cards left, so there are only 49! ways to arrange those.
Similarly, the number of ways to make a flush (a hand where all of the cards are of the same suit) is
C(13,5) = 13! / (5! * 8!) = 1287
This is because there are 13 choices for our first card (out of a total of 13 clubs), 12 choices for our second card (out of a total of 12 clubs), 11 choices for our third card (out of a total of 11 clubs), 10 choices for our fourth card (out of a total of 10 clubs), and 9 choices for our fifth card (out of a total of 9 clubs). And again we divide by 5! because once we’ve chosen our five cards, there are only 5 clubs left, so there are only 5! ways to arrange those.
The number of ways to make any given hand in poker can be calculated using the above formula. For example, the number of ways to make a full house (a hand with three matching cards and two matching cards) is
C(13,3) * C(4,2) * C(12,1) * C(4,1) = 3744.
PRO TIP:There are 6,169,740 possible 7 card poker hands. Of those hands, only 2,598,960 are distinct. This means if you were to make every possible 7 card hand, there would be only 2,598,960 unique combinations.
A full house consists of three matching cards and two matching cards. There are C(13,3) ways to choose our three matching cards (out of a total of 13 possible choices), C(4,2) ways to choose which two ranks those cards will have (out of a total 4 possible ranks), C(12,1) ways to choose our non-matching rank (out of a total 12 possible ranks), and C(4,1) ways to choose which suit that rank will have (out of a total 4 possible suits).
So altogether there are 3744 different full houses that can be made. .
The numberof different 7-card poker hands is:C(52 7)= 2 598 960.
9 Related Question Answers Found
When it comes to playing poker with a group of friends, one of the most important things to consider is how many poker chips you’ll need for the game. While there’s no one-size-fits-all answer to this question, there are some general guidelines you can follow to ensure that you have enough chips to keep the game going smoothly and without any interruptions. In this article, we’ll take a look at how many poker chips you need for 7 players, and offer some tips on how to make sure that your chip supply is adequate for the game.
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