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

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 .