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Math Help - probability

  1. #1
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    probability

    (i) how many different poker hands can be dealt to a player?
    (ii) how many hands include the Ace of spades?
    (iii) how many hands do not contain include the ace of spades?
    (iv)how many hands include all 4 aces?
    (v) how many hands contain exactly 3 aces?


    so i know that there are 52 cards in a pack and that a poker hand is 5 cards, so the answer to (i) is 52 choose 5 52C5 , using the calculator i get 2598960.

    and i know that there is only one ace of spades in a pack of cards but i'm not quite sure how to work out part (ii) and if i knew the answer to this then obviously i could work out the answer to part (iii)

    could anyone give me a bit of help please? thanks.
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  2. #2
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    Re: probability

    Hello, amyl95!

    (1) How many different poker hands can be dealt to a player?
    You are correct!

    There are: . {52\choose5} \:=\:\frac{52!}{5!\,47!} \:=\:2,\!598,\!960 possible hands.




    (2) How many hands include the Ace of Spades?
    We want the A\spadesuit and four of the 51 other cards.

    . . 1\cdot{51\choose4} \:=\:249,\!900




    (3) How many hands do not contain the Ace of Spades?
    We want 5 of the other 51 cards.

    . . {51\choose5} \:=\:2,\!349,\!060




    (4) How many hands include all 4 Aces?
    There is one way to have all four Aces.
    And we want one of the other 48 cards.

    . . 1\cdot{48\choose1} \:=\:48




    (5) How many hands contain exactly 3 Aces?

    There are {4\choose3} choices for the three Aces.
    And there are {48\choose2} ways to choose the other two cards.

    . . {4\choose3}{48\choose2} \:=\:4\cdot 1128 \:=\:4512
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  3. #3
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    Re: probability

    thanks so much I'm new to probability so I need all the help I can get.
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