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Thread: contest

  1. #1
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    contest

    There is a contest. 5 students will attend to this contest. 6 different books will be given as the prize. Winner will get 3 books, seond 2 books, and third student will get 1 book. In how many ways we can distribute the prizes?

    My work:
    C(6,3).C(3,2).C(2,1)

    But the answer is 3600 according to the book.
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  2. #2
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    Re: contest

    5 ways of picking 1st place winner
    4 ways of picking 2nd place winner
    3 ways of picking 3rd place winner
    $\dbinom{6}{3}$ ways of choosing 3 books for 1st place
    $\dbinom{3}{2}$ ways to choose 2 books for 2nd place
    $\dbinom{1}{1}$ way to choose 1 book for 3rd place
    Product principle says since each step is independent from the previous steps, take the product.
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  3. #3
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    Re: contest

    I also found 60. Book's answer is wrong.
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    Re: contest

    Quote Originally Posted by kastamonu View Post
    I also found 60. Book's answer is wrong.
    No, the book is correct. By the product principle, the number of ways to distribute the prizes is:
    $5\cdot 4\cdot 3\cdot \dbinom{6}{3}\cdot \dbinom{3}{2}\cdot \dbinom{1}{1} = 3600$
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  5. #5
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    Re: contest

    Correct I only distributed the books. Many Thanks.
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    Re: contest

    Quote Originally Posted by kastamonu View Post
    There is a contest. 5 students will attend to this contest. 6 different books will be given as the prize. Winner will get 3 books, seond 2 books, and third student will get 1 book. In how many ways we can distribute the prizes?
    My work:
    C(6,3).C(3,2).C(2,1) But the answer is 3600 according to the book.
    Take six blank cards. Mark a one on three of them; mark a two on two of them; mark a one on one card.
    How many ways can those marked cards is a row?
    $\dfrac{6!}{3!\cdot 2!\cdot 1!}=60$ SEE HERE
    Last edited by Plato; Jun 2nd 2017 at 03:31 PM.
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