How many ways to get a Four of a kind?

• gillgill
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.
gillgill
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?

Hmm, a flash review of your answers suggests to me you are correct

-- AI

You seem to know what you're doing gillgill. So why the doubt?

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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