Positive integral solutions of a linear equation for JEE

Formula

\(x_1+x_2+\cdots+x_n=r\) has \(\,{}^{r-1}C_{n-1}\) solutions

Variables: \(x_1,x_2,\dots,x_n\) are positive integers.

Conditions: \(r\ge n\ge 1\).

Distribution of identical objects with each box non-empty.