How many ways to get a Four of a kind?

  • Thread starter gillgill
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In summary, there are 624 ways to obtain four of a kind, 3744 ways to obtain a full house, and 123,552 ways to obtain two pairs. In a game where only three cards are dealt, there are 3744 ways to obtain one pair, and in a game where four cards are dealt, there are 164736 ways to obtain one pair. Your answers seem to be correct.
  • #1
gillgill
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Poker hands...

1. How many ways are there to obtain these three highly-rated combinations below?
a. Four of a kind. -Four cards of the same rank and one other card

b. Full House. -Three cards of the same rank and two cards both of another rank. ( A triple, or three of a kind, and a pair.)

c. Two pairs. -Two pairs of cards of two distinct ranks and a fifth card of another rank.

2. Suppose you play a game in which only three cards are deal: How many ways are there to obtain one pair?

3. Suppose four cards are dealt. How many ways are there to obtain one pair?

am i doing these correctly?
1a. 13C1 X 48C1 = 624
b.13C1 X 4C3 X 12C1 X 4C2 = 3744
c.13C2 X 4C2 4C2 44C1 = 123,552

2.13C1 X 4C2 X 12C1 X 4C1 = 3744

3. 13C1 X 4C2 X 12C1 X 4C1 X 11C1 X 4C1 = 164736

am i right?
 
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  • #2
Hmm, a flash review of your answers suggests to me you are correct

-- AI
 
  • #3
You seem to know what you're doing gillgill. So why the doubt?
 
  • #4
thanks...
 

1. How many ways can you get a Four of a kind in a standard deck of 52 cards?

In a standard deck of 52 cards, there are 13 different ranks (2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace) and 4 suits (clubs, diamonds, hearts, spades). Therefore, there are 13 possible Four of a kind combinations, one for each rank. This means that there are 13 ways to get a Four of a kind in a standard deck of 52 cards.

2. What is the probability of getting a Four of a kind in a 5-card poker hand?

The probability of getting a Four of a kind in a 5-card poker hand is approximately 0.024%, or 1 in 4,165. This is calculated by taking the number of possible Four of a kind combinations (13) and dividing it by the total number of 5-card poker hands (2,598,960).

3. Can you get a Four of a kind in a game of Texas Hold'em?

Yes, it is possible to get a Four of a kind in a game of Texas Hold'em. However, the chances of getting a Four of a kind in this game are significantly lower than in a 5-card poker hand, as players only use 5 community cards out of a standard deck of 52 cards. The probability of getting a Four of a kind in Texas Hold'em is approximately 0.02%, or 1 in 4,950.

4. How does the number of decks used in a game affect the chances of getting a Four of a kind?

The number of decks used in a game does not significantly affect the chances of getting a Four of a kind. This is because the probability of getting a Four of a kind is based on the number of possible combinations in a standard deck of 52 cards, rather than the number of decks used in a game. However, if multiple decks are used, the chances of getting a Four of a kind may be slightly higher as there are more cards in play.

5. Is it possible to get more than one Four of a kind in a single hand?

No, it is not possible to get more than one Four of a kind in a single hand. This is because there are only 4 cards of each rank in a standard deck of 52 cards, so there can only be a maximum of 4 of a kind in any given hand.

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