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Math Help - [SOLVED] Is this right? card problem

  1. #1
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    [SOLVED] Is this right? card problem

    a deck has 52 cards, 12 face cards and 4 aces are removed, from these 16 cards 4 are chosen, how many combinations are possible that have at least 2 black cards.

    The answer is 1302

    I get 154?
    What I did was,

    there are 8 black cards so,

    8c2+8c3+8c4=154
    I could swear I did this right.
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  2. #2
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    wait I think it's 8c2 times 8c2 ....


    Yes it is.

    I figured it out....
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  3. #3
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    Hello, brentwoodbc!

    You're forgetting about the red cards . . .


    A deck has 52 cards.
    12 face cards and 4 aces are removed.
    From these 16 cards, 4 are chosen.
    How many combinations are possible that have at least 2 black cards?

    The answer is 1302.

    To get "at least 2 Blacks", we want: .(2 Black, 2 Red) or (3 Black, 1 Red) or (4 Black).

    . . There are: . (_8C_2)(_8C_2) = 784 ways to get 2 Black, 2 Red.

    . . There are: . (_8C_3)(_8C_1) = 448 ways to get 3 Black, 1 Red.

    . . There are: . _8C_4 = 70 ways to get 4 Black.


    Therefore, there are: . 784 + 448 + 70 \:=\:1302 ways to get at least 2 Blacks.

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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, brentwoodbc!

    You're forgetting about the red cards . . .



    To get "at least 2 Blacks", we want: .(2 Black, 2 Red) or (3 Black, 1 Red) or (4 Black).

    . . There are: . (_8C_2)(_8C_2) = 784 ways to get 2 Black, 2 Red.

    . . There are: . (_8C_3)(_8C_1) = 448 ways to get 3 Black, 1 Red.

    . . There are: . _8C_4 = 70 ways to get 4 Black.


    Therefore, there are: . 784 + 448 + 70 \:=\:1302 ways to get at least 2 Blacks.

    Ya I know thank you.
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