Question

You have 8 posters to hang in your room. You want to hang the posters as a border around the walls of your room. How many ways can you arrange the posters?

a. 8
b. 01
c. 40,320
d. 64

Answer 1

To determine the number of ways to arrange 8 posters, calculate the factorial of 8 (8!), which equals 40,320. Thus, the correct answer is option c, 40,320.

Step-by-step explanation:

The student is asking about the number of different ways you can arrange 8 posters around a room. This type of problem is a permutation problem because the order in which the posters are arranged matters. To find the number of arrangements for n unique items, you use the factorial of n, which is n!, and represents the product of all positive integers up to n.

For this particular case, you would calculate the factorial of 8, which is 8!. This calculation would be 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, which equals 40,320. Therefore, there are 40,320 different ways to arrange the posters, so the correct answer would be option c, 40,320.