Find solutions of this equation If $a+b+c+d = 30$ and $a,b,c,d$ lie between $0$ and $9$. How to find number of solutions of this equation.

Hint: Consider the coefficient of $x^{30}$ in
$$
\left(\frac{x^{10}-1}{x-1}\right)^4
$$
Since
$$
(1-x)^{-4}=\sum_{n=0}^\infty\binom{n+3}{3}x^n
$$
and
$$
\left(1-x^{10}\right)^4=\sum_{k=0}^4(-1)^k\binom{4}{k}x^{10k}
$$
we get the coefficient of $x^n$ to be
$$
\sum_{k=0}^4(-1)^k\binom{4}{k}\binom{n-10k+3}{n-10k}
$$
Note that $\binom{n-10k+3}{n-10k}=\binom{n-10k+3}{3}$ when $n\ge10k$.
