1. Multiset

Would a question such as:
How many non-negative integer solutions are there to
x + y + z = 10?
be worked out as a multiset question?

I worked it out like this:
C(3+10-1,3) = C(12,3) = 220

Is this correct? If it's incorrect what is the proper way to solve these kinds of questions?

2. Originally Posted by Lupin
Would a question such as:
How many non-negative integer solutions are there to
x + y + z = 10?
be worked out as a multiset question?
I worked it out like this:
C(3+10-1,3) = C(12,9) = 220
Is this correct? If it's incorrect what is the proper way to solve these kinds of questions?
No. It should be $\binom{10+3-1}{10}=\binom{10+3-1}{3-1}$

The multiset rule is: To make K selections from N different items is done in $\binom{K+N-1}{K}=\binom{K+N-1}{N-1}$ ways.

In this problem K=10 & N=3.

3. Thank you! I got it all figured out now.