Number of non negative integral solutions for $a + b + c = n$
Where $n$ is a positive integer are
$$\binom{n + 3 - 1}{3 - 1}$$
But if a condition is there $a > b > c$
Is there any direct method by which we can find out required number of solutions.
I believe that we should multiply original number of solutions by $1 / 4$ as there are four following cases possible $a = b > c$
$a = b = c$
$a > b = c$
$a > b > c$