Question 118127This question is from textbook Introductory Statistics
: Please help me with the following problem:
A poker hand consistes of 5 cards dealt from an ordinary deck of 52 playing cards.
a). How many poker hands are possible?
b). How many different hands consisting of three kings and two queens are possible?
c). The hand in part (b) is an example of a full house: 3 cards of one denomination and 2 of another. How many different full houses are possible?
d). Calculate the probability of being dealt a full house.
This is dealing with the counting rules and using the combination rule and the permutations rule.
Thank you for your help.
This question is from textbook Introductory Statistics
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A poker hand consistes of 5 cards dealt from an ordinary deck of 52 playing cards.
a). How many poker hands are possible?
52C5 = 2,598,960
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b). How many different hands consisting of three kings and two queens are possible?
[4C3*4C2] = 4*6 = 24
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c). The hand in part (b) is an example of a full house: 3 cards of one denomination and 2 of another. How many different full houses are possible?
Pick a card type: 13 ways
Pick 3 of the 4 cards: 4C3=4
Pick a 2nd card type: 12 ways
Pick 2 of the 4 cards: 4C2= 6
Total = 13*12*4*6 = 3744 full houses possible.
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d). Calculate the probability of being dealt a full house.
3744/2,598,960
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Cheers,
Stan H.
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