Total Possible Poker Hands

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Algebra -> Probability-and-statistics-> SOLUTION: A five-card poker hand is dealt at random from a standard 52-card deck. Note the total number of possible hands is C(52,5)=2,598,960. Find the probabilities of the following sc Log On

How many full house poker hands are there? There are a total of 3,744 poker hands that can result in a full house. This can be calculated by multiplying the total number of card choices: Total No. Of Card Choices = 13 (choices for 3 same cards) x 12 (choices for 2 cards that are the same = 156. By the total number of suit choices. There are 10 possible 5 card poker hands: royal flush, straight flush, four of a kind, full house, flush, straight, three of a kind, two pair, one pair, high card. There are 1,326 possible 2 card starting hands in Texas Hold'em. The types of 3-card poker hands are straight flush 3-of-a-kind straight flush a pair high card The total number of 3-card poker hands is. A straight flush is completely determined once the smallest card in the straight flush is known. There are 48 cards eligible to be the smallest card in a straight flush. Hence, there are 48 straight flushes.

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Question 1067265: A five-card poker hand is dealt at random from a standard 52-card deck.
Note the total number of possible hands is C(52,5)=2,598,960.
Find the probabilities of the following scenarios:
(a) What is the probability that the hand contains exactly one ace? Answer= α/C(52,5), where α=_______
(b) What is the probability that the hand is a flush? (That is all the cards are of the same suit: hearts, clubs, spades or diamonds.) Answer= β/C(52,5), where β=_______
(c) What is the probability that the hand is a straight flush? Answer= γ/C(52,5), where γ=________
All help is very much appreciated! :) Thank you!
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A five-card poker hand is dealt at random from a standard 52-card deck.
Note the total number of possible hands is C(52,5)=2,598,960.
Find the probabilities of the following scenarios:
(a) What is the probability that the hand contains exactly one ace? Answer= α/C(52,5), where α= 4C1 = 4
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(b) What is the probability that the hand is a flush? (That is all the cards are of the same suit: hearts, clubs, spades or diamonds.) Answer= β/C(52,5),
where β = 4*13C5
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(c) What is the probability that the hand is a straight flush? Answer= γ/C(52,5), where γ = (8 fluses*4 suits) = 32
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Cheers,
Stan H.
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All Possible Poker Hands