Question

23. There are 42 runners in a race, and no ties. In how many ways can the first three finishers be chosen from the 42 runners, regardless of how they are arranged?

Answer 1

As given by the question

There are given that 42 runners in a race

Now,

First three finishers be chosen from the 42 runners

So, the combination will be:

`42_(C_3)`

Then

`\begin{gathered} 42_(C_3)=(42!)/((42-3)!*3!) \\ =(42!)/((39)!*3!) \\ =(42*41*40*39!)/((39)!*3!) \\ =(42*41*40)/(6) \\ =7*41*40 \\ =11480 \end{gathered}`