Hello, mathlover14!

Note: The following doesanswer the question.not

If the order of the addendsconsidered, there is a simple approach.is

Consider:

Place the 8 objects in a row, leaving a space between them.

. . There are: spaces.

. .

Select 2 of the 7 spaces and insert "dividers".

. . There are: dividers.

. .

This diagram represents:

If the orderconsidered, the number of ways is:is

Can we eliminate the duplication included in this method?

I don't know . . . I've tried and failed.