Table of Contents
- 1 How many different ways can 5 cards be dealt from a deck of 52?
- 2 How many ways are there to select a 5 card poker hand from a standard deck of 52 cards such that at least one of the cards is a club?
- 3 How many 5 card poker hands have at least one of every suit?
- 4 How many ways are there to draw a hand of cards that have at least two different suits?
- 5 How many cards are there in a deck of cards?
- 6 How many possible flushes are there in poker?
How many different ways can 5 cards be dealt from a deck of 52?
2598960 different ways
(52−5)! 5! = 2598960 different ways to choose 5 cards from the available 52 cards.
How many ways are there to select a 5 card poker hand from a standard deck of 52 cards such that at least one of the cards is a club?
So that’s 13C2 * 13C1 * 13C1 * 13C1 * 4 = 685,464 out of the 52C5 = 2,598,960 possible poker hands.
How many different five card hands have all five cards of a single suit?
There are 2,598,960 different combinations of five card poker hands. That is 52*51*50*49*48 divided by 5*4*3*2. Four of those combinations are Royal Flushes. 10,JQKA all of the same suit.
How many hands are there with at most 5 cards?
Hence, there are 40 straight flushes. 4-of-a-kind hands. full houses. choices for 5 cards in the same suit….Abstract:
| hand | number | Probability |
|---|---|---|
| straight flush | 40 | .000015 |
| 4-of-a-kind | 624 | .00024 |
| full house | 3,744 | .00144 |
| flush | 5,108 | .0020 |
How many 5 card poker hands have at least one of every suit?
There are 5⋅4⋅3 ways to assign the suits to the values. That gives us 4⋅(135)⋅5⋅4⋅3=308880 such hands in total.
How many ways are there to draw a hand of cards that have at least two different suits?
A hand with two suits has either four cards from one suit and one from the other, or three cards from one suit and two from the other. There are 12 ways to choose the major and minor suits. For each (ordered) pair of suits, there are (134)(131)+(133)(132)=31603 ways to make a hand; the result is 12×31603=379236 again.
How many 5-card poker hands are in a deck?
The number of 5-card poker hands from a standard deck is (52 | 5) (read: “52 pick 5”) as there are 52 cards and you’re picking 5 of them. [There’s an easier notation for the above, but I dunno how to type it in plain text.] Anyway, that is a combinatorial and calculates out to 2,598,960 unique hands.
How many 5-card hands are there in 4*C(13)5?
For any one of the four suits, there are C (13,5) 5-card hands… i.e. the number of combinations of taking 5 cards from 13 distinct cards. But, since there are 4 suits, there are then 4*C (13,5) possible “flushes.”
How many cards are there in a deck of cards?
In a standard deck of cards, there are 4 possible suits (clubs, diamonds, hearts, spades),and 13 possible values (2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace). Let A, J, Q, Krepresent Ace, Jack, Queen and King, respectively. Every card has a suit and value, and everycombination is possible. Hence a standard deck contains 13·4 = 52 cards.
How many possible flushes are there in poker?
For any one of the four suits, there are C (13,5) 5-card hands… i.e. the number of combinations of taking 5 cards from 13 distinct cards. But, since there are 4 suits, there are then 4*C (13,5) possible “flushes.” Thus, there are 4*1287=5148 possible flushes in poker.