8. The number of non-negative integer solutions to the equation $2 x_{1}+x_{2}+x_{3}+x_{4}+x_{5}+x_{6}+x_{7}+x_{8}+x_{9}+x_{10}=3$ is
$\qquad$ groups.
When $x_{1}=0$, the number of non-negative integer solutions for $x_{2}+x_{3}+\cdots+x_{10}=3$ is $C_{11}^{3}=165$; when $x_{1}=1$, the number of non-negative integer solutions for $x_{2}+x_{3}+\cdots+x_{10}=1$ is $C_{9}^{1}=9$. Therefore, the number of non-negative integer solutions for the equation $2 x_{1}+x_{2}+x_{3}+\cdots+x_{10}=3$ is $165+9=174$.