Small towns frequently erect signs in the fields alongside the highway to encourage passersby to stop and shop. If each of 8 businesses place one sign in a line along the side of the highway, in how many different orders might the signs be arranged?

To calculate the number of different orders in which the 8 signs can be arranged, you can use the concept of permutations. In this case, you have 8 businesses, and you want to arrange their signs in a line alongside the highway. The number of different orders is given by 8 factorial, denoted as 8!.

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320

So, there are 40,320 different orders in which the signs can be arranged along the side of the highway, each representing a unique arrangement of businesses' signs to encourage passersby to stop and shop.

Permutations are a fundamental concept in combinatorics, representing the different ways you can arrange a set of objects. The factorial notation, such as 8!, is commonly used to express permutations. It's essential for solving problems involving order and arrangement of elements.

Learn more about different orders

brainly.com/question/35965041

#SPJ11