Integral Solutions
- Number of positive integral solutions to $$x_{1}+x_{2}+x_{3}+.....+ x_{n}=s $$ where s>=0 is $$ ^{s-1}\textrm{C}_{n-1} $$
- Number of non-negative integral solutions to $$x_{1}+x_{2}+x_{3}+.....+ x_{n}=s $$ where s>=0 is $$ ^{n+s-1}\textrm{C}_{n-1} $$
