Question

A) 6 men a,b,c,d,e,f are to be seated around a circular table. How many ways are there of achieveing this if a refuses to sit besides b?

Answer 1

We divide this in two parts,

Firstly, we seat 5 people  B,C,D,E,F   ; as they have no restrictions. Total number of ways of doing so are 4!  

Secondly, we select a seat for  A   , such that it is not next to  B. There are 5 seats for  A   , out of which 2 are next to  B           . Therefore, the number of ways of selecting a seat is (3/1).

      Now, using the Rule of Product (or Fundamental Counting Principle), we get the total number of ways in which all six people can sit

4! * (3/1) = 24 * 3 = 72