Question

Six sprinters have made it to the Olympic finals in the 100-meter race. In how many different ways can the
gold, silver and bronze medals be awarded (rounded off to zero decimals)?

Answer 1

We need to choose 3 medallists among 6 athletes. Since all medals are different, we can do it in

$\displaystyle C(6,3) = \begin{pmatrix}6\\3\end{pmatrix}=\frac{6!}{3!3!} = \frac{4 \cdot 5 \cdot 6}{1\cdot 2 \cdot 3} = 20$ ways.

Answer: 20 ways