Non-negative integral solutions of a linear equation for JEE

Formula

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

Variables: \(x_1,x_2,\dots,x_n\) are non-negative integers.

Conditions: \(r\ge 0, n\ge 1\).

Distribution of identical objects, stars and bars, integer solution counting.