For $m, n ∈ \Bbb N, m ≥ 1$, let $S(m, n)$ be the number of solutions to the equation: $x_1 + x_2 + \cdots + x_m = n$, where $x_i ∈ \Bbb N$ for $i = 1, \ldots , m$. Using induction, prove that for all, $m, n \in\Bbb N, m ≥ 1$, $$S(m, n) = \frac{(n + m − 1)!}{(m − 1)!\,n!}$$
I am unable to solve this question, any contribution is highly appreciated.