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Home Q & A Board Science-Related Homework Help Mathematics
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Darrien Darrien
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10 years ago
How many different hands consist of three kings and two queens are possible?The hand in part (b) is an example of a full house 3:cards of one denomination and 2 of another./Howmany diffent full houses are possible?calculate the probability of being dealt a full house.
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SMITHAM2SMITHAM2
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10 years ago
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10 years ago
I disagree with the earlier analysis because it doesn't matter what order you get the cards in.  There are four combinations of three kings (club, diamond, heart; club, diamond, spade; club, heart, spade; diamond, heart, spade) and six combinations of two queens (CD, CH, CS, DH, DS, HS).  Thus, there are 24 combinations that create a full house of kings over queens.  This number can get multiplied by 169, which gives you 4056 possible full houses dealt from five cards.

The question then becomes the number of possible combinations of dealing out five cards.  That number is 52*51*50*49*48/5*4*3*2*1, which comes out 2598960.  The reason you divide it by 5 factorial is because it doesn't matter what order the cards come in.  Thus, the odds of being dealt kings full of queens is 24/2598960, while the odds of being dealt any full house is 4056/2598960, which is approximately .15%, or about 1 in 700.

Hope this helps.
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