SOLUTION: 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?

Algebra ->  Permutations -> SOLUTION: 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?      Log On


   

Question 1056671: 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?
Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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.