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Math Help - Binominal cooefficient wording of a question

  1. #1
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    Binominal cooefficient wording of a question

    How many different 5-card hands can be dealt from a standard 52-card deck?

    I've highlighted the word different because I believe it's the key to the question, am I right in thinking the answer is

    52*51*50*49*48 = 311,875,200
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    Re: Binominal cooefficient wording of a question

    Quote Originally Posted by uperkurk View Post
    How many different 5-card hands can be dealt from a standard 52-card deck?
    If the question means "how many ways can you be dealt a five card hand?", then the answer is \binom{52}{5}=2598960.

    Or does it have another meaning?
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    Re: Binominal cooefficient wording of a question

    Well I don't know that is just how the question is written but

    23456
    23465
    23654
    26543
    65432

    would all be classes as a different hand? I am not sure.
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    Re: Binominal cooefficient wording of a question

    Quote Originally Posted by uperkurk View Post
    Well I don't know that is just how the question is written but
    23456
    23465
    23654
    26543
    65432
    would all be classes as a different hand? I am not sure.
    No. That is incorrect. Order makes no difference. Consider only content.
    \boxed{A\spadesuit}~\boxed{2\clubsuit}~\boxed{6 \spadesuit}~\boxed{10 \heartsuit}~\boxed{8 \diamondsuit} is the same hand in any order.
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  5. #5
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    Re: Binominal cooefficient wording of a question

    No, they wouldn't. Your answer, 52*51*50*49*48, which is the same as \frac{52!}{47!} or _{52}P_5 which includes the same cards in different orders. To not count the same cards in different orders as different hands, you need to divide by 5!, the number of orders of the same 5 cards. That will give you \frac{52*51*50*49*48}{5!} which is exactly \frac{52!}{5! 47!}= \begin{pmatrix}52 \\ 5\end{pmatrix} as Plato said.
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    Re: Binominal cooefficient wording of a question

    ok thanks for explaining
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