The number of possible fullhouses is 13*12*6*4. See why?.
The total number of 5 card hands is C(52,5).
In poker a Full House is a hand consisting of 3 cards of one kind and 2 cards of another kind. For example, 'eights and fives' is a hand consisting of 3 eights and 2 fives. hat is the probability of being dealt a full house from a standard deck of 52 cards if the dealing is done fairly?
Here ya go . . .
We want a Triple and a Pair.What is the probability of being dealt a Full House?
There are 13 choices of value for the Triple.
There are: . ways to get the Triple.
There 12 choices for the value of the Pair.
There are: . ways to get the Pair.
Hence, there are: . Full Houses.
There are: . possible five-card hands.
13 is the # of suits.
6 is the number of combinations possible for the pairs, i.e. 2 cards from 4 choices.
4 is the # of each card type that would get 3 of a kind.
12 is the card types left after one is used up for the 3 of a kind.
So, we have 13*6*4*12=3744