Question

inspecting restaurants how many different ways can a city health department inspector visit 6 restaurants in a city with 14 restaurants? the number of different ways the inspector can visit 6 out of 14 restaurants is

Explanation:

Step1: Identify as permutation problem

We use the permutation formula $P(n,r)=\frac{n!}{(n - r)!}$, where $n = 14$ (total number of restaurants) and $r=6$ (number of restaurants to visit).

Step2: Calculate factorial values

$n!=14! = 14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1$, $(n - r)!=(14 - 6)!=8!=8\times7\times6\times5\times4\times3\times2\times1$. Then $P(14,6)=\frac{14!}{(14 - 6)!}=\frac{14!}{8!}=\frac{14\times13\times12\times11\times10\times9\times8!}{8!}$.

Step3: Simplify the expression

Canceling out the $8!$ terms, we get $P(14,6)=14\times13\times12\times11\times10\times9 = 2162160$.

Answer:

$2162160$