Originally Posted by

**nukenuts** Find the number of non-negative integer solutions of the inequality

x1 + x2 + x3 + x4 + x5 + x6 < 10.

Answer:

If this was -

Find the number of non-negative integer solutions of the equation

x1 + x2 + x3 + x4 + x5 + x6 **=** 10

I would view this as having 10 identical items to distribute among 6 people and would use $\displaystyle \binom{10+6-1}{10}$.

However Im not sure how to handle it with when it's an equality. Would I write it as a summation formula?

$\displaystyle \color{blue}\sum_{n=0}^9 {n+6-1\choose n}$