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Thread: How many ways can 5-card hands be dealt to include exactly 3 diamonds?

  1. #1
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    How many ways can 5-card hands be dealt to include exactly 3 diamonds?

    A standard deck of cards consists of 4 suits (spades,hearts,diamonds,clubs) of 13 cards each. In how many ways can 5-card hands be dealt that include 3 diamonds and 2 cards from other suits ?

    My answer is : [tex]C_{13}^{3}ŚC_{39}^{2}[/tex]
    Is it correct ?
    Last edited by Alfredo Dawlabany; 02-07-2018 at 06:43 AM.

  2. #2
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    Quote Originally Posted by Alfredo Dawlabany View Post
    A standard deck of cards consists of 4 suits (spades,hearts,diamonds,clubs) of 13 cards each. In how many ways can 5-card hands be dealt that include 3 diamonds and 2 cards from other suits ?

    My answer is : [tex]C_{13}^{3}ŚC_{39}^{2}[/tex]
    Is it correct ?
    Correct, assuming your notation is non-standard, namely the last of the C forms listed here. I would write it as C(13,3)*C(39,2).

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