in a race in which five automobiles are entered and there are no ties, in how many ways can the first three…
in a race in which five automobiles are entered and there are no ties, in how many ways can the first three finishers come in?\nways
Answer
Explanation:
Step1: Identify permutation formula
The problem is about permutations. The formula for permutations of $n$ objects taken $r$ at a time is $P(n,r)=\frac{n!}{(n - r)!}$. Here $n = 5$ (number of automobiles) and $r=3$ (number of first - three finishers).
Step2: Calculate factorial values
We know that $n!=n\times(n - 1)\times\cdots\times1$. So, $5! = 5\times4\times3\times2\times1=120$ and $(5 - 3)!=2!=2\times1 = 2$.
Step3: Substitute values into formula
$P(5,3)=\frac{5!}{(5 - 3)!}=\frac{120}{2}=60$.
Answer:
60