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## Homework Statement

a) Given x

_{1}+x

_{2}+x

_{3}=20, for all positive integers, how many solutions are there?

b) For x > 3?

## Homework Equations

Multichooose

## The Attempt at a Solution

At first I computed "20 multi-choose 3" and got 231, but I believe that is counting zeros as part of the solutions.

So for the positive integers I computed "19 Multichoose 3" and go 210.

For x > 3 I computed "17 Multichoose 3" and got 171.

We looked at the method of counting say 5 multichoose 2 would be thought of as xlxxlxx, which is how many ways can you arrange two l's in 7 slots, or 7C2. So I have a decent understand how the multichoose function works but not so confident in my answers. I feel the x > 0 is correct.