Question

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 & the other end is the top.

a) If all components are different, how many different designs are possible?
b) If 7 components are the same, & others are different, how many different designs are possible?
c) If 3 components are of one type, and 4 of another, and other 5 are different, how many different designs are possible?

Answer 1

Combination refers to the selection of items without the regards to order of how they are selected. Permutation is the opposite. It has regards to order in the arrangement.
To answer:
a) For 12 different components the rule for permutations (all possible orderings) is n! = n(n-1)(n-2)...
b) 12!/7! (since 7! are repeated)
c) 12!/(3! 4! 5!) ... divide by repeated.