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Math Help - combinatorics

  1. #1
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    combinatorics

    Suppose there are 3 jobs which are to be assigned to 5 mans where each man can be assigned more than 1 job.
    How many ways are there to assign the 3 jobs?

    My answer is C(5+3-1,3) and my lecturer gives the answer 5^3.
    Can anyone comment on this?
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  2. #2
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    The first job can be assigned to any of 5 men.
    The 2nd job can be assigned to any of 5 men.
    The 3rd job can be assigned to any of 5 men.

    The number of possibilities are 5 x 5 x 5.
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  3. #3
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    Hello, problem!

    Suppose there are 3 jobs which are to be assigned to 5 men
    where each man can be assigned more than 1 job.
    How many ways are there to assign the 3 jobs?

    My answer is C(5+3-1,\:3)
    and my lecturer gives the answer 5^3.
    Can anyone comment on this?
    Here is your lecturer's reasoning:

    With no additional restrictions, all 5 jobs could be given to one man.

    So, for each of the 3 jobs, there are 5 choices for a man to assign it to.

    Therefore, there are: . 5 \times5\times 5 \:=\:5^3 possible job assignments.

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  4. #4
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    Quote Originally Posted by problem View Post
    Suppose there are 3 jobs which are to be assigned to 5 mans where each man can be assigned more than 1 job.
    How many ways are there to assign the 3 jobs?

    My answer is C(5+3-1,3) and my lecturer gives the answer 5^3.
    Can anyone comment on this?
    Your solution of \binom{5+3-1}{3} would have been correct if the jobs were indistinguishable, i.e., if we only cared how many jobs each person received as opposed to which jobs they received. But that does not appear to be the case in this particular problem. Does that clear it up any?
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