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?

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.