a) Given x1+x2+x3=20, for all positive integers, how many solutions are there?
b) For x > 3?
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.