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.
a. if all components are different, how many different designs are possible (i think this is just 12!)
b. If seven components are identical to one another, but the other are different, how many different designs are possible? (i think 12!/7! but not sure why)
c. if three components are of one t ype and identical to one another, and four components are of another type and identical to one another, but the others are different, how many different designs are possible? (this one is the one I'm really stuck on)