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Distributing objects

  1. Nov 17, 2008 #1

    tgt

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    1. The problem statement, all variables and given/known data
    If we like to distribute 3 pears and 4 apples to 9 people such that no 2 or more fruit is given to the same person, in how many ways can this be done?


    3. The attempt at a solution
    (9,7)[(7,3)-(6!/4!+5!/3!)] where (a,b) represents the 'a choose b' function.
     
  2. jcsd
  3. Nov 18, 2008 #2

    tiny-tim

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    Hi tgt! :smile:
    urgh! :yuck:

    Hint: let's rewrite the question …

    we want to distribute 3 pears and 4 apples and 2 nothings to 9 people so that they get one each. :wink:
     
  4. Nov 18, 2008 #3

    tgt

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    No. A person is allowed to have two pieces of fruit such as one pear and one apple.
     
  5. Nov 18, 2008 #4

    tiny-tim

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    Are you sure?

    You originally quoted:
    which includes "no 2 fruit is given to the same person" …

    in other words, one or none each. :confused:
     
  6. Nov 18, 2008 #5

    HallsofIvy

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    tiny-tim, I would interpret "no 2 or more fruit" as meaning each person gets either 0 or 1 fruit of any kind- so "one pear and one apple" wou.ld violate that. And I would interpret "A gets an apple" as different from "A gets a pear". That's a noticeably harder problem.
     
  7. Nov 18, 2008 #6

    tgt

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    It seems both HallsoIvy and tiny tim are correct. In which case the answer is 9!/(2!3!4!)

    But that's not a noticeable hard problem, hallsofivy?
     
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