Answer
$56$
Work Step by Step
The number of arrangement of choosing $r$ objects out of $n$ distinct object $(r \leq n)$ is:
$(a)$ If order matters, use permutation, i.e, $P(n, r)$.
$(b)$ If order doesn't matter, use combination, i.e, $C(n, r)$.
Order doesn't matter since once 3 professors are chosen for the committee, no matter how you arrange them, they are still the same 3 professors.
Therefore, $C(8, 3) = \frac{P(8, 3)}{3!} = \frac{336}{6} = 56$
