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Math Help - card deck word problem

  1. #1
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    card deck word problem

    question:

    we pull 6 cards from a standard deck of 52.

    a) how many ways can we end up with all 6 being spades?

    b) how many ways can we end up with 2 aces, 3 kings, and a queen?

    if my notes are right (i don't think they are) part "a" would be 52 choose 6 and part "b" would be 52 choose 5.
    can someone confirm or deny this please?
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  2. #2
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    Hello, graffitihead!

    We pull 6 cards from a standard deck of 52.

    a) How many ways can we end up with all 6 being Spades?

    There are 13 Spades; we want 6 of them.

    There are: . {13\choose6} \:=\:\frac{13!}{6!\,7!} \:=\:1716 ways.



    b) How many ways can we end up with 2 Aces, 3 Kings, and a Queen?

    \begin{array}{ccc}\text{There are four Aces; we want two of them: } & {4\choose2} \:=\:6\text{ ways} \\ \\[-3mm]<br /> <br />
\text{There are four Kings; we want three of them:} & {4\choose3} \:=\:4\text{ ways} \\ \\[-3mm]<br /> <br />
\text{There are four Queens; we want one of them: } & {4\choose1} \:=\:4 \text{ ways} \end{array}


    Therefore, there are: . 6 \cdot 4 \cdot 4 \;=\;96 ways.

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  3. #3
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    thx

    thanks for your help!
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