Poker Hands Permutations Combinations

3/17/2022 admin

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Suppose you have 1 card: A. There's only one way you can put it in order.
If you have two cards A and B, you can arrange them in two different ways. They can be AB or BA.
With three cards A,B and C there are six different ways: ABC, ACB, BAC, BCA, CAB, CBA

The way the numbers arrive is that for one card it's 1. For two cards it's 2x1=2 and for three cards it's 3x2x1=6. The quick way to write 3x2x1 is 3! The ! sign is called a factorial. Some calculators (including the one found on computers) have a special ! button.

How many different 5 card poker hands can be formed from a deck of 52 cards? This is obviously related to the number of permutations. If we start with all the possible permutations of 5 cards out of 52, the answer would be Number = 52(51)(50)(49)(48)=311,875,200. When dealt a poker hand during a game, order does not matter so you will have the same hand regardless of the order in which the cards are dealt. Combination problems involve such scenarios. To approach such a question, begin with the permutations: how many possible poker hands are there, if order does matter? In poker, players form sets of five playing cards, called hands, according to the rules of the game. Each hand has a rank, which is compared against the ranks of other hands participating in the showdown to decide who wins the pot. In high games, like Texas hold 'em and seven-card stud, the highest-ranking hands win. All possible combinations of card/poker hands for a set of players. Ask Question Asked 6 years. Like combinations and permutations but without luck. 1 I know the usual approach to poker hands using combinations. For example the probability for a pair in a 5 card hand is (13 1) (4 2) (12 3) ∗ 4 3 (52 5).

Poker Hands Permutations Combinations Chart

Let's move on a bit.

If you've got four cards you can arrange them in 4! = 24 ways.
If you've got five cards you can arrange them in 5! = 120 ways.
If you've got six cards you can arrange them in 6! ways = 720 ways.

Get ready for the BIG numbers!

The number of ways you can arrange 10 cards is 3,628,800
The number of ways you can arrange 13 cards is 6,227,020,800
The number of ways you can arrange 20 cards is 2,432,902,008,176,640,000. That's two and a half billion billion.

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So how many ways can you order all the 52 cards in a pack?

The sum is 52x51x50x49x48....x4x3x2x1 and the answer is:

80,658,175,170,943,878,571,660,636, 856,403,766,975,289,505,440, 883,277,824,000,000,000,000

That's roughly the same as an 8 with 67 zeros after it.

To put this in perspective, the dinosaurs died out 65,000,000 years ago, and the age of the earth is just 4,500,000,000 years. Now suppose everybody in the world was to arrange packs of cards at the rate of one per second, it would take 600,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years to get all the combinations! That's why you're VERY unlikely ever to shuffle a pack of cards the same way twice.

Other pages of interest:

There are more card facts and big numbers at Chances of Card Hands

More game numbers and stats at The Roulette Wheel - and How to Worry the Casino!

Suppose you have 1 card: A. There's only one way you can put it in order.
If you have two cards A and B, you can arrange them in two different ways. They can be AB or BA.
With three cards A,B and C there are six different ways: ABC, ACB, BAC, BCA, CAB, CBA

Poker Hands Permutations Combinations Calculator

The way the numbers arrive is that for one card it's 1. For two cards it's 2x1=2 and for three cards it's 3x2x1=6. The quick way to write 3x2x1 is 3! The ! sign is called a Poker hands permutations combinations worksheet

Poker hands permutations combinations worksheet

factorial. Some calculators (including the one found on computers) have a special ! button.