Question

A qualifying race includes 12 female athletes. The top 3 finishers will represent the U.S. on the olympic 10K team. How many possible different teams are there?

Answer 1

The number of combinations of the 12 athletes taken 3 at a time is:
\[\large 12C3=\frac{12!}{3!(12-3)!}=\frac{12\times11\times10}{3\times2\times1}=2\times11\times10\]