Answer
The number of different ways in which the first three finishers come in a race Is 120.
Work Step by Step
The first three finishers come in from a competition of 6 automobiles. Te order in which the finishers win the race matters because each finisher will finish with a different rank and there are no ties. Therefore, we need to find the number of permutations of 6 things taken 3 at a time.
Apply the formula,
${}_{n}{{P}_{r}}=\frac{n!}{\left( n-r \right)!}$
Where $ n=6,r=3$
$\begin{align}
& {}_{6}{{P}_{3}}=\frac{6!}{\left( 6-3 \right)!} \\
& =\frac{6!}{3!}
\end{align}$
Solve further the solution to get,
$\begin{align}
& _{6}{{P}_{3}}=\frac{6\times 5\times 4\times 3!}{3!} \\
& =6\times 5\times 4 \\
& =120
\end{align}$
