An insect starts at the origin $(0,0,0)$ of a 3D grid. At each step, it moves 1 unit in the positive $x$, $y$, or $z$ direction with equal probability. Given that the insect reaches the point $(2,2,1)$ in exactly 5 steps, what is the probability that its path did not pass through either $(1,1,0)$ or $(1,1,1)$?