10. Among the students in the second year of junior high school, 32 students participated in the math competition, 27 students participated in the English competition, and 22 students participated in the Chinese competition. Among them, 12 students participated in both math and English, 14 students participated in both English and Chinese, and 10 students participated in both math and Chinese. It is known that $\frac{5}{8}$ of the students who participated in the competitions won awards. How many students won awards?
10. Let the number of people who participate in all three subjects be $x$, and the total number of participants be $y$, then
$$
\begin{aligned}
y & =32+27+22-12-14-10+x \\
& =45+x .
\end{aligned}
$$

Given $2 \leqslant x \leqslant 10$, hence $47 \leqslant y \leqslant 55$.
Only when $y=48$, it can be divisible by 8, so the number of award winners is $48 \times \frac{5}{8}=30$ (people).