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# PLZ HELP

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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

### 2+0 Answers

#1
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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

Dec 30, 2018
#2
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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

Dec 30, 2018
edited by CPhill  Dec 30, 2018