Question

test marketing products anderson research company decides to test - market a product in 9 areas. how many different ways can 3 areas be selected in a certain order for the first test? there are ways to select 3 out of 9 areas.

Explanation:

Step1: Identify permutation formula

The formula for permutations is $P(n,r)=\frac{n!}{(n - r)!}$, where $n$ is the total number of items and $r$ is the number of items to be selected in a certain order. Here $n = 9$ and $r=3$.

Step2: Calculate factorial values

$n!=9! = 9\times8\times7\times6\times5\times4\times3\times2\times1$, $(n - r)!=(9 - 3)!=6!=6\times5\times4\times3\times2\times1$. Then $P(9,3)=\frac{9!}{6!}=\frac{9\times8\times7\times6!}{6!}$.

Step3: Simplify the expression

Cancel out the $6!$ terms. We get $P(9,3)=9\times8\times7=504$.

Answer:

504