Answer
The number of ways in which the first four finishers come in out of 6 competitors is $360$.
Work Step by Step
We know that from the information,
$\begin{align}
& n=10 \\
& r=4 \\
\end{align}$
Then, we have to find the number of permutations of 6 things taken 4 at a time by applying the above formula:
$\begin{align}
& {}_{6}{{P}_{4}}=\frac{6!}{\left( 6-4 \right)!} \\
& =\frac{6!}{2!} \\
& =\frac{6\times 5\times 4\times 3\times 2!}{2!} \\
& =360
\end{align}$
Thus, there are $360$ ways.
