Question

your two parents have driven to work in separate cars. when they arrive, there are nine empty spaces in the parking lot. they each choose a parking space. how many outcomes are possible?
there are \\(\square\\) possible ways to park their cars.
(type a whole number)

Explanation:

Step1: Use permutation formula

The number of permutations of \(n\) objects taken \(r\) at a time is \(P(n,r)=\frac{n!}{(n - r)!}\). Here \(n = 9\) (total empty spaces) and \(r=2\) (number of cars to park).

Step2: Calculate factorial values

\(n!=9! = 9\times8\times7\times6\times5\times4\times3\times2\times1\), \((n - r)!=(9 - 2)!=7! = 7\times6\times5\times4\times3\times2\times1\). Then \(P(9,2)=\frac{9!}{7!}=\frac{9\times8\times7!}{7!}\).

Step3: Simplify the expression

Cancel out the \(7!\) terms. So \(P(9,2)=9\times8=72\).

Answer:

72