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?

Guest Dec 30, 2018

#1**-1 **

We can do 12 choose 2, which looks like this: \(\frac{12!}{10!2!}=\frac{12\times 11}{2}=66\)

Therefore, there are 66 different ways.

You are very welcome!

:P

CoolStuffYT Dec 30, 2018

#2**+1 **

Note that this is just a permute of all the possible sets of choosing any 2 things from 12

Note that each set will be (Satrap, Vizier)....and for any two people we choose, we have two possible arrangements for each set...

So....the number of possible sets = 2 * (12C2) = 132 possibilities

CPhill Dec 30, 2018