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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?

 Dec 30, 2018

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!


 Dec 30, 2018

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



cool cool cool

 Dec 30, 2018
edited by CPhill  Dec 30, 2018

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