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Math Help - How Many Possibilities?

  1. #1
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    How Many Possibilities?

    Suppose five cards are drawn from a standard (52 card) deck of cards. From the 5 cards chosen, 3 are red and 2 are black. How many possibilities are there for this hand?
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    Quote Originally Posted by magentarita View Post
    Suppose five cards are drawn from a standard (52 card) deck of cards. From the 5 cards chosen, 3 are red and 2 are black. How many possibilities are there for this hand?
    There are twenty-six red and twenty-six black cards.
    Choose three reds and two blacks.
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  3. #3
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    do you...

    Quote Originally Posted by Plato View Post
    There are twenty-six red and twenty-six black cards.
    Choose three reds and two blacks.
    You mean 3/26 + 2/26 or 3/26 times 2/26?
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    Combinatorics question

    Hello magentarita
    Quote Originally Posted by magentarita View Post
    You mean 3/26 + 2/26 or 3/26 times 2/26?
    Neither. Plato means choose 3 from 26 and then 2 from 26. So the total number of choices is

    \binom{26}{3}\times\binom{26}{2} = 845000

    Grandad
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    Quote Originally Posted by magentarita View Post
    You mean 3/26 + 2/26 or 3/26 times 2/26?
    Neither of those.
    \binom{26}{3}\cdot \binom{26}{2}
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