Problem - 122
Let $a > b > c$ be three positive integers. If their remainders are $2$, $7$, and $9$ respectively when being divided by $11$. Find the remainder when $(a+b+c)(a-b)(b-c)$ is divided by $11$.
$$(a+b+c)(a-b)(b-c)\equiv (2+7+9)(2-7)(7-9)\equiv 180\equiv \boxed{4}\pmod{11}$$