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Math Help - Combination/Permutation Problem

  1. #1
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    Angry Combination/Permutation Problem

    A television director is scheduling a certain sponsor's commercials for an upcoming broadcast. There are six slots available for commercials. In how many ways may the director schedule the commercials?

    a) If the sponsor has 6 different commercials, each to be shown 1 time?
    (This one I know is 6!)
    b) If the sponsor has 3 different commercials, each to be shown 2 times?
    From here onwards I don't know how to approach the question.
    c) If the sponsor has 2 different commercials, each to be shown 3 times?

    d) If the sponsor has 3 different commercials, the first of which is to be shown 3 times, the second 2 times and the third 1 time?

    Can anyone please explain how to answer this question, thanks.
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  2. #2
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    Hello, ibetan!

    A television director is scheduling a certain sponsor's commercials
    for an upcoming broadcast. There are six slots available for commercials.
    In how many ways may the director schedule the commercials?

    a) If the sponsor has 6 different commercials, each to be shown 1 time?

    (This one I know is 6!) . Good!

    b) If the sponsor has 3 different commercials, each to be shown 2 times?
    Call the commercials: . \{A,A,B,B,C,C\}

    Then there are: . {6\choose2,2,2} \:=\:90 ways.



    c) If the sponsor has 2 different commercials, each to be shown 3 times?
    Call the commercials: . \{A,A,A,B,B,B\}

    Then there are: . {6\choose3,3} \:=\:20 ways.



    d) If the sponsor has 3 different commercials, the first is to be shown 3 times,
    the second 2 times and the third 1 time?
    Call the commericals: . \{A,A,A,B,B,C\}

    Then there are: . {6\choose3,2,1} \:=\:60 ways.

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, ibetan!




    Call the commercials: . \{A,A,B,B,C,C\}

    Then there are: . {6\choose2,2,2} \:=\:90 ways.



    Call the commercials: . \{A,A,A,B,B,B\}

    Then there are: . {6\choose3,3} \:=\:20 ways.



    Call the commericals: . \{A,A,A,B,B,C\}

    Then there are: . {6\choose3,2,1} \:=\:60 ways.

    I dont get why to use combinations? Can you explain please.
    the answer to b) 6C4*4C2=90

    I found the same answers using permutations n!/a!b!c!

    Edit: I used left side equals right side and they are equal equations. But I dont understand the reasoning behind using combinations for this question.
    Last edited by ibetan; March 7th 2010 at 07:19 AM.
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  4. #4
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    [QUOTE=ibetan;470061]I dont get why to use combinations? Can you explain please. the answer to b) 6C4*4C2=90[QUOTE]
    Those are not combinations. The notation \binom{N}{a,b,c} is rarely used in textbooks today.
    In stands for permutations with repetitions \binom{N}{a,b,c}=\frac{N}{a!b!c!}.
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