Question 1056671
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in how many ways can 20 board members sit in a circular board room if the chairman must sit between the secretary and the treasure?
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In problems like this one the two arrangements are considered as undistinguished (as one unique arrangement) 
if there is a rotation which maps one arrangement to the other.


Based on this agreement, the number of different arrangements is 

2*(20-3)! = 2*17!


The factor "2" describes two different placements for the secretary and the treasure.


17! is the number of different arrangements for the rest 20-3 = 17 members.