4. (1) Given the equation $x+y+z=15$, find the number of natural number solutions.
(2) The equation $2 x_{1}+x_{2}+x_{3}+x_{4}+x_{5}+x_{6}+$ $x_{7}+x_{8}+x_{9}+x_{10}=3$ has how many non-negative integer solutions?
4. (1) The number of solutions in natural numbers is $C_{14}^{2}=91$.
(2) Classify by $x_{1}$:
(i) When $x_{1}=1$, there are 9 non-negative integer solutions.
(ii) When $x_{1}=0$, there are 165 non-negative integer solutions. From (i) and (ii), the original equation has $9+165=174$ non-negative integer solutions.