Question

Skylar is arranging 8 objects on a shelf. How many different ways can she arrange them? How can I figure this out using the formula for combinations?

Answer 1

Using the formula for combinations, Skylar can arrange the 8 objects in 1 different way.

Step-by-step explanation:

To find the number of different ways Skylar can arrange the 8 objects, we can use the formula for combinations. The formula for combinations is n! / (r!(n-r)!), where n is the total number objects and r is the number of objects being arranged. In this case, n = 8 and r = 8, so the formula becomes 8! / (8!(8-8)!), which simplifies to 8! / (8! x 0!). Since 0! is equal to 1, the formula becomes 8! / 8! x 1. Any number divided by itself is equal to 1, so the formula simplifies further to 1 x 1, which is equal to 1. Therefore, there is only 1 way Skylar can arrange the 8 objects.

Answer 2

Personally, I never bothered learning the formula.
When I run into a problem like this, I look at it this way:
(I learned this method from my high school math teacher,
Mr. H. Carlisle Taylor, in 1956. It not only works, but I can
even understand it !)

The first object can be any one of the 8 . For each of those ...
The 2nd object can be any one of the other 7. For each of those ...
The 3rd object can be any one of the other 6 . For each of those ...
The 4th object can be any one of the other 5 . For each of those ...
The 5th object can be any one of the other 4 . For each of those ...
The 6th object can be any one of the other 3 . For each of those ...
The 7th object can be any one of the other 2 . For each of those ...
The 8th object has to be the 1 that's left.

Total number of possible ways to line them up is

(8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = 40,320 ways .