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How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books ?

How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books ? Correct Answer 9

The correct answer is option 4.

Key Points

Here, there are six copies of the same book into four identical boxes(same box). We will enumerate all ways to pack the books. For each way to pack the books, we will list the number of books in the box with the largest number of books, followed by the numbers of books in each box containing at least one book, in order of decreasing the number of books in abox

6,0,0,0 
5,1,0,0
4,2,0,0
4,1,1,0
3,3,0,0
3,2,1,0
3,1,1,1
2,2,2,0
2,2,1,1.

So the total number of ways is 9.

∴ Hence the correct answer is 9.

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