Answer:
There are 252 different ways Jaime can arrange five posters out of his ten on his closet door.
Explanation:
This is a classic example of a combination problem, where we want to choose a certain number of objects from a larger set without regard to their order. In this case, Jaime wants to choose 5 posters out of the 10 he has, and the order in which he puts them on his door doesn't matter.
The formula for the number of combinations of n objects taken r at a time is:
nCr = n! / (r! * (n-r)!)
where n is the total number of items, r is the number of items we want to choose, and ! means factorial, which is the product of all positive integers up to that number. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
Using this formula, we can find the number of ways Jaime can choose 5 posters out of his 10:
10C5 = 10! / (5! * (10-5)!)
= (10 * 9 * 8 * 7 * 6) / (5 * 4 * 3 * 2 * 1)
= 252
So, there are 252 different ways Jaime can arrange five posters out of his ten on his closet door.