Hello and thank you in advance for any help you may be able to give me!
I am stuck on the following question:
A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards.
a) How many poker hands are possible?
b) How many different hands consisting of 3 kings and 2 queens are possible? c) A full house consists of 3 cards of one denomination and 2 cards of another. How many different full houses are possible?
d) Calculate the probability of being dealt a full house.
On "a" I am stuck on 2 different answers. My first answer I figured c1*c1-1*c1-2*c1-3*c1-4= 52*51*50*49*48= 311,875,200 because I figured every time you dealt a card, there was one less card to be dealt in the deck. However, looking around different sites I keep seeing that the answer to part "a" is c(52,5) = 2,598,960. So now I don't know which is correct.
As for parts b-d I'm completely lost!
Thanks again for any help!!!
Thanks... I think I finally understand. So basically it's 52!/5! 47! so I multiply 52x51x50x49x48x47!, then cancel out both 47!'s, which gives me 311,875,200 and then I divide by 5! (5x4x3x2x1) (120) and voila! It's 2,598,960. Thanks again for the help! I forgot about the cancellation so I was making it extra hard by doing all of these problems the long way (52x52x50x49x48x47x46x46x44........x2x1) Talk about frustrating!