# How many five-card poker hands consisting of three of a kind and a pair are possible?

## How many five-card poker hands consisting of three of a kind and a pair are possible?

Probability of Three of a Kind First, count the number of five-card hands that can be dealt from a standard deck of 52 cards. We did this previously, and found that there are 2,598,960 distinct poker hands. Next, count the number of ways that five cards can be dealt to produce three of a kind.

How many 5 card hands are possible where each card is a face card?

The number of poker hands containing all face cards are different combinations of those 12 cards in hands of 5 cards. = 12!/( 7! * 5!) = 792 hands.

### How many 5 card hands are there consisting of 3 face cards 1 King and 1 spade?

How many 5-card hands are there consisting of 3 face cards, 1 king, and 1 spade? From a deck of 52-playing cards, 5 cards are drawn. How many 5-card hands are there consisting of 3 face cards, 1 king, and 1 spade? Hence, the total number of ways is 896+48=944 ways.

How many 5 card hands are there consisting of 3 face cards one king and one spade?

## How many five card poker hands consisting of all hearts are possible How many five card poker hands consisting of all cards of the same suit are possible?

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.

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How many hands contain 3 of a kind?

858 54,912
Frequency of 5-card poker hands

Hand Distinct hands Frequency
Three of a kind 858 54,912
Two pair 858 123,552
One pair 2,860 1,098,240
No pair / High card 1,277 1,302,540

### How many 5-card poker hands can be drawn from a deck?

The only difference is the order in which the cards are dealt. These are the same hand. Order is not important. The number of possible 5-card poker hands would then be the same as the number of 5-element subsets of 52 objects. The following is the total number of 5-card poker hands drawn from a standard deck of 52 cards.

How many 4-of-a-kind hands are there in poker?

There are 40 cards eligible to be the smallest card in a straight flush. Hence, there are 40 straight flushes. In forming a 4-of-a-kind hand, there are 13 choices for the rank of the quads, 1 choice for the 4 cards of the given rank, and 48 choices for the remaining card. This implies there are 4-of-a-kind hands.

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## How many 5-card hands with 5 cards in sequence?

There are 10 five-consecutive sequences in 13 cards (as shown in the explanation for straight flush in this section). In each such sequence, there are 4 choices for each card (one for each suit). Thus the number of 5-card hands with 5 cards in sequence is. Then we need to subtract the number of straight flushes (40) from this number.

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.