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!

Hint: for any type of problem see how many ways you can put the number of plus signs thinking it as a divider in the set of $n$ points.
Let us take the first problem. Here you have $4$ plus signs and have $8$ dots. So the total number of possibility  is  $$\binom{8+5-1}{5-1}$$
and the resulting 4 groups of dots will then correspond to the $4$ variables you reqd.
