## Precalculus (6th Edition) Blitzer

The number of ways in which the first four finishers come in out of 6 competitors is $360$.
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.