If where are non negative integers , then how many possible outcome are there ?
It is basic counting problem, we solve it by adding an extra non-negative integer such that , and then use star and bars . Hence the answer is .
However , there is something that stuck in my mind such that why are we adding only one extra variable , to be clearer , why dont we add more than one extra variable. For example , why did not i find the solution of where the extra terms and are non-negative, too. Briefly, why did we restrict ourselved with only one extra variable? Can you enlighten me ?