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  1. #1
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    10 books are arranged on a shelf randomly...




    10 books are arranged on a shelf randomly.

    A) What's the probability that between the books "Cinderella" and "The Hobbit" 3 books exactly will seperate them?

    I tried to do 9!*4!*2! divided by 10!

    But..the answer doesn't make sense, that's 480%!

    Help?


    B) Among the 10 books, 4 have red covers, 4 with blue and 2 with white. What's the probability that all books from the same colour are next to each other?

    Here I tried to do 3!*4!*4*2! = 6912

    Then 3! = 6 (because the order of what colours doesn't matter)

    then 6912*6 = 41472

    Then 41472 divided by 10! (which is all possible arrangements) I get = 0.011

    Makes sense?

    -nerd_girl (AKA April)

  2. #2
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    A) C is Cinderella and H is Hobbit. The subset CBBBH has 5 elements and there are 6 possible locations for them in the set of 10 books, and 8! ways to arrange the remaining 8 books for each of these 6 positions

    CBBBHBBBBB
    BCBBBHBBBB
    BBCBBBHBBB
    BBBCBBBHBB
    BBBBCBBBHB
    BBBBBCBBBH

    so that there are 8!*6*2 = 483840 ways 3 books can separate C and H (C and H can be interchanged, hence factor of 2). Then

    P(3 books in between C and H) = 483840 / 10! = .134

    B) I think you included a factor of 6 twice on accident. Divide your answer by 6 and it should be good.

  3. #3
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    Should we also consider HBBBC?
    Quote Originally Posted by zmogggggg View Post
    A) C is Cinderella and H is Hobbit. The subset CBBBH has 5 elements and there are 6 possible locations for them in the set of 10 books, and 8! ways to arrange the remaining 8 books for each of these 6 positions

    CBBBHBBBBB
    BCBBBHBBBB
    BBCBBBHBBB
    BBBCBBBHBB
    BBBBCBBBHB
    BBBBBCBBBH

    so that there are 8!*6*2 = 483840 ways 3 books can separate C and H (C and H can be interchanged, hence factor of 2). Then

    P(3 books in between C and H) = 483840 / 10! = .134

    B) I think you included a factor of 6 twice on accident. Divide your answer by 6 and it should be good.

  4. #4
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    Quote Originally Posted by semic View Post
    Should we also consider HBBBC?
    The factor of 2 considers this.

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