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Math Help - Counting problem; Why is Instructor's solution correct?

  1. #1
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    Counting problem; Why is Instructor's solution correct?

    How many ways can 9 identical DVDs be packed into 3 identical boxes if
    (a) each box may contain any number of DVDs?

    My instructor told me the following was correct: 1 box: {9}, 2 boxes: {8,1} {7,2} {6,3} {5,4}, 3 boxes: {7,1,1} { 6,2,1} {5,2,2} {4,3,2} {3,3,3}

    1+4+5 = 10 ways.

    My question is: Why can't 3 boxes have {3,1,5} or {4,1,4} ? Or is my instructor incorrect? Thanks.
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  2. #2
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    Re: Counting problem; Why is Instructor's solution correct?

    Quote Originally Posted by Walshy View Post
    How many ways can 9 identical DVDs be packed into 3 identical boxes if
    (a) each box may contain any number of DVDs?
    My instructor told me the following was correct: 1 box: {9}, 2 boxes: {8,1} {7,2} {6,3} {5,4}, 3 boxes: {7,1,1} { 6,2,1} {5,2,2} {4,3,2} {3,3,3}
    1+4+5 = 10 ways.
    My question is: Why can't 3 boxes have {3,1,5} or {4,1,4} ? Or is my instructor incorrect? Thanks.
    You are correct the as is 12.
    This is a well-known problem which takes many forms.
    It is counting the number of ways a positive integer, N, can be partitioned into k or fewer summands, P(N,k).

    Example: P(4,2)=3~: 4,~3+1,~2+2

    P(9,3)=12.

    Tell your instructor to read chapter six of MATHEMATICS OF CHOICE by Ivan Niven.
    Thanks from Walshy
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