Question

Queen Zubaida wishes to choose a Satrap and a Vizier from among her $12$ courtiers. How many different ways can she assign the two roles, assuming the same person cannot fulfill both roles?

Answer 1

The order Queen Zubaida picks a Satrap and a Vizier does not matter. Since order does not matter, combination is used. 

Using a calculator, we solve for nCr = 12C2 = 66 ways..

Or using the combination formula C(n,r) = n!/[(n-r)!r!] 
C(12, 2) = 12!/[(10!)(2!)] = 66 ways.