2. 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.
2. Obviously, $x_{1}$ can only take 1 or 0.

When $x_{1}=1$, the original equation has 9 solutions.
When $x_{1}=0$, the solutions of the original equation that contain the digit 3 have 9 groups, those that do not contain 3 but contain 2 have 72 groups, and those that only contain 1 and 0 have $C_{9}^{3}=84$ groups.
Therefore, the total number of non-negative integer solutions is 174.