How many ways are there to pack six copies of the same book into four…

Final answer: 9 ways.

Reasoning: Boxes are identical and books are identical, so each packing corresponds to an integer partition of 6 into at most 4 positive parts (empty boxes are allowed). Count these partitions.

The partitions of 6 with at most 4 parts are:

• 6

• 5 + 1

• 4 + 2

• 4 + 1 + 1

• 3 + 3

• 3 + 2 + 1

• 3 + 1 + 1 + 1

• 2 + 2 + 2

• 2 + 2 + 1 + 1

There are 9 partitions in this list, so there are 9 distinct ways to pack the six identical books into four identical boxes.