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

132 ways

Explanation:

Queen Zubaida can choose any of 12 people for her Satrap. Once she has made that selection, she can choose any of the remaining 11 people as her Vizier. Thus, the number of ways she can assign both roles is…

Answer 2

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.