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# probability

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suppose you are dealt 5 cards from a standard 52 card deck. determine the probability of being dealt a full house

a. how many ways can 5 cards be selected from a 52 card deck?

Guest Mar 31, 2017
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#1
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Idk, how?

Cole_2  Mar 31, 2017
#2
+79835
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P(Full House)

We  want to choose any 1 of the13 ranks....and from this rank we want to choose any 3 of 4 cards

Then,  we want to choose any one of the 12 remaining ranks and choose any 2 of 4 cards from this rank

So we have

C(13, 1) * C (4,3) * C(12,1) * C(4,2)  /  C(52, 5)      where C(52, 5)  represents the number of ways of choosing any 5 cards from 52 = 2598960

So   we have

3744 / 2598960  =   6 / 4165    ≈  0.00144  ≈  .144%

CPhill  Mar 31, 2017

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