Question

A half-marathon has 53 runners. A first-, second-, and third-place trophy will be awarded. Howmany different ways can the trophies be awarded?

Answer 1

Let's use the combination formula:

`\begin{gathered} C(n,k)=nCk=(n!)/(k!(n-k)!) \\ n=53 \\ k=3 \\ C(53,3)=53C3=(53!)/(3!(50)!)=23426 \end{gathered}`