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

$\begin{gathered} 42_{C_3}=\frac{42!}{(42-3)!\times3!} \\ =\frac{42!}{(39)!\times3!} \\ =\frac{42\times41\times40\times39!}{(39)!\times3!} \\ =\frac{42\times41\times40}{6} \\ =7\times41\times40 \\ =11480 \end{gathered}$