8. The sum of the ages of three people, A, B, and C, represented by $x, y, z$ is 120, and $x, y, z \in (20,60)$. The number of ordered triples $(x, y, z)$ is $\qquad$ .
8.1 141 .

Notice a basic conclusion:
The number of positive integer solutions $(a, b, c)$ to the indeterminate equation $a+b+c=n$ is $\mathrm{C}_{n-1}^{2}$.
Thus, the number of solutions to the indeterminate equation
$$
(x-20)+(y-20)+(z-20)=60
$$

satisfying $x, y, z>20$ is $\mathrm{C}_{59}^{2}$.
Among these $\mathrm{C}_{59}^{2}$ solutions, the number of solutions where $x \geqslant 60$ and do not meet the requirements is
$$
(x-59)+(y-20)+(z-20)=21
$$

satisfying $x \geqslant 60, y, z>20$ is $\mathrm{C}_{20}^{2}$.
Similarly, the number of solutions where $y \geqslant 60$ is $\mathrm{C}_{20}^{2}$, and the number of solutions where $z \geqslant 60$ is $\mathrm{C}_{20}^{2}$.

Since no two can simultaneously reach 60, the number of ordered triples $(x, y, z)$ is $\mathrm{C}_{59}^{2}-3 \mathrm{C}_{20}^{2}=1141$.