Wilson's theorem

Statement

Wilson’s theorem states that if $p$ is prime then $(p-1)!\equiv -1\pmod p$. Use it to find the remainder of $10!$ upon division by $11$.

Solution

Since $11$ is prime, Wilson gives $10!\equiv -1\equiv 11-1\equiv \boxed{10}\pmod{11}.$ (Check: $10!=3628800=11\cdot 329890+10$.)