6. Find the number of non-negative integer solutions of the following inequality:
$$
x+y+z+u \leq 20 .
$$
6. Ans: 10626
Let $v=20-(x+y+z+u)$. Then $v \geq 0$ if and only if $x+y+z+u \leq 20$. Hence the answer is equal to the number of non-negative integer solutions of the following equation:
$$
x+y+z+u+v=20
$$
and the answer is $\binom{24}{4}=10626$.