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?
+129847 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%
