N committee members sit at a round table. K different organisations have representatives on the committee. How many ways can the members be seated subject to the constraint that each organisation has...

1. 
   

   
   
   N
   
   committee members sit at a round table.
   
   K
   
   different organisations have representatives on the committee. How many ways can the members be seated subject to the constraint that each organisation has a varying membership of at least one representative and when it has more than one then no two of them may sit next to each other?
   

   
   

(The answer is provided by the chromatic polynomial of the circuit of length

n,



C,.:

PB{C..)

= (k-1)"+(-l)"(k-1))