Results 1 to 5 of 5

Math Help - Probability of Poker Hands

  1. #1
    Newbie
    Joined
    Sep 2007
    Posts
    3

    Probability of Poker Hands

    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!!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Shanynn View Post
    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!!!
    a) you are counting each permutation of a hand as a distinct hand when
    they are in fact the same hand.

    Therefore the number of distinct hands is 311,875,200/(5!)= 2,598,960.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2007
    Posts
    3
    I feel like such an idiot, but I still can't figure out how to get 2,598,960 as my answer. What are the steps that lead to that answer? Probabilities is driving me crazy!!!!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Shanynn View Post
    I feel like such an idiot, but I still can't figure out how to get 2,598,960 as my answer. What are the steps that lead to that answer? Probabilities is driving me crazy!!!!
    there are 52 cards in the deck. you want to find the number of ways you can choose 5 cards from those. hence it is the combination _{52}C_5 = {52 \choose 5} = 2598960
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2007
    Posts
    3

    Finally get it!

    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!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. poker hands
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: December 1st 2011, 07:09 PM
  2. Combinatorics - Poker Hands
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 8th 2008, 12:08 PM
  3. Different Poker Hands Question
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: September 20th 2007, 07:21 AM
  4. Probability (with Bridge Hands)
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: September 17th 2007, 04:47 AM
  5. Probability (Bridge Hands)
    Posted in the Statistics Forum
    Replies: 3
    Last Post: September 14th 2007, 11:18 PM

Search Tags


/mathhelpforum @mathhelpforum