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

#2**+1 **

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