I am having some trouble understanding the difference between two questions. Here is the first question:
A printed circuit board has eight different locations in which a component can be placed. If four different components are to be placed on the board, how many different designs are possible?
Answer: P(8,4) = 1680 ways
In the design of an electromechanical product, 12 components are to be stacked into a cylindrical casing in a manner that minimizes the impact of shocks. One end of the casing is designated as the bottom and the other end is the top. If all components are different, how many different designs are possible.
Answer: 12! = 479001600 designs
Why is it 12! and not P(12,7)?