AMC 12 2025a Problem 18

How many ordered triples $(x, y, z)$ of different positive integers less than or equal to $8$ satisfy $xy > z$, $xz > y$, and $yz > x$?

\textbf{(A)}~36 \textbf{(B)}~84 \textbf{(C)}~186 \textbf{(D)}~336 \textbf{(E)}~486