Henry's little brother has $8$ identical stickers and $4$ identical sheets of paper. how many ways are there for him to put all of the stickers on the sheets of paper, if only the number of stickers on each sheet matters?

The easiest way to visualize and answer this is to list all possible combinations or arrangements on the 4 sheets of paper.

Take note that the arrangement is as following:

# of stickers on sheet 1 - # of stickers on sheet 2 - # of stickers on sheet 3 - # of stickers on sheet 4

8 – 0 – 0 – 0

7 – 1 – 0 – 0

6 – 2 – 0 – 0

6 – 1 – 1 – 0

5 – 3 – 0 – 0

5 – 2 – 1 – 0

5 – 1 – 1 – 1

4 – 4 – 0 – 0

4 – 3 – 1 – 0

4 – 2 – 2 – 0

4 – 2 – 1 – 1

3 – 3 – 2 – 0

3 – 3 – 1 – 1

3 – 2 – 2 – 1

2 – 2 – 2 – 2

Therefore there are a total combinations of 15 arrangements of stickers on sheets of paper.

2x^2+5x+17

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