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Math Help - Permutation and Combination Help!

  1. #1
    Member looi76's Avatar
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    Permutation and Combination Help!

    Question:

    Eight cards are selected with replacement from a standard pack of 52 playing cards, with 12 picture cards, 20 odd cards and 20 even cards.
    (a) How many different sequences of eight cards are possible?
    (b) How many of the sequences in part (a) will contain three pictures, three odd-numbered cards and two even-numbered cards?
    (c) Use parts (a) and (b) to determine the probability of getting three picture cards, three odd-numbered cards and two even-numbered cards if eight cards are selected with replacement from a standard pack of 52 playing cards.


    Attempt:
    NO IDEA! Please Help!
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  2. #2
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    a.)

    a.) Start out with 52 cards taken eight at a time (52C8)
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  3. #3
    Member looi76's Avatar
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    Quote Originally Posted by digitalis77 View Post
    a.) Start out with 52 cards taken eight at a time (52C8)

    I did that and got 752538150 but the answer in the text book is 5.346\times10^{13}. I am confused!
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  4. #4
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    dont those #s match
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  5. #5
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    nevermind those #s dont match. what level math are you in?
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  6. #6
    Member looi76's Avatar
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    Quote Originally Posted by digitalis77 View Post
    nevermind those #s dont match. what level math are you in?
    GCE AS-Level Maths
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  7. #7
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    Quote Originally Posted by looi76 View Post
    Question:

    Eight cards are selected with replacement from a standard pack of 52 playing cards, with 12 picture cards, 20 odd cards and 20 even cards.
    (a) How many different sequences of eight cards are possible?
    (b) How many of the sequences in part (a) will contain three pictures, three odd-numbered cards and two even-numbered cards?
    (c) Use parts (a) and (b) to determine the probability of getting three picture cards, three odd-numbered cards and two even-numbered cards if eight cards are selected with replacement from a standard pack of 52 playing cards.
    You both missed the bold red above.
    a) {52}^8 = 53459728531456
    b)  ({12}^3)({20}^3)({20}^2)(8!)<br />
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