Find all non-negative integers satisfying the conditions 
Question 1. Find all non-negative integer a, b, c,d, e such that $$ a+b+c+d+e = 8$$



Question 2. Find all non-negative integer a, b, c,d such that $$ a+b+c+d = 8$$



Question 3. Find all non-negative integer a, b, c such that $$a+b+c = 8$$


Is there any method for this? I have no idea. I can just fix the limit. Thanks!
I think must calculate on Maple or Sage math program. I hope that that someone can help. 
Thanks!

The problem is asking to find all the partitions (with a specified number of parts).
You want to partition the number 8 in 5, 4, and 3 pieces, so the answer is in the section "Restricted part size or number of parts" of that wikipedia page.
Here is a maple example
