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.