Question 132
Real numbers $a$, $b$, and $c$ have arithmetic mean $0$. The arithmetic mean of $a^2$, $b^2$, and $c^2$ is $10$. What is the arithmetic mean of $ab$, $ac$, and $bc$?
$(A)$ $-5$ $(B)$ $-\frac{10}{3}$ $(C)$ $-\frac{10}{9}$ $(D)$ $0$ $(E)$ $\frac{10}{9}$
$(A)$ $-5$ $(B)$ $-\frac{10}{3}$ $(C)$ $-\frac{10}{9}$ $(D)$ $0$ $(E)$ $\frac{10}{9}$