Question

How many different combinations of two can be made from 80 people?

Answer 1

Plugging directly into the combination formula, the answer is $\binom{80}{2}=\frac{80!}{2!78!}=\frac{80\cdot 79}{2\cdot 1}=40\cdot 79=\boxed{3160},$ where we have cancelled out common factors.