Question

How many solutions does the equation a + b + c + d + e + f + g ≤ 50 have if each variable must be a non-negative integer?

Answer 1

Do you need to write a program to figure this out? Looks like a Stats/combinatorics problem to me.

a = 50 and b=c=d=e=f=g=0
a = 49, b=1 and c=d=e=f=g=0

and so on.

You need some combination of factorials. Any ideas?

Answer 2

If you still need an answer for this and noone here can help you try to find Khan Academy videos on combinations/permutations. That should sort you out.