Question

a college has 5 instructors qualified to teach a special computer lab course that requires 2 instructors to be present. how many different pairs of teachers could teach the class?

Answer 1

Notice that teacher A and teacher B can be paired up in two "distinct" ways, AB and BA. Since it's really the same pair, this means order doesn't matter, so you use the combination formula:
\[\large{}_5C_2=\frac{5!}{2!(5-2)!}\]