Eight friends A,B,C,D,E,F,G,H are sitting around a circular table numbered 1 to 8. A and F sit together. B and D never sit adjacent to each other. H and G sit opposite to each other. What is the total number of ways in which these people can be seated?

• P(never seat together)=1-P(seat together)
  
  CIRCULAR PERMUTATION=(n-1)! =7!
  A and B can interchange their positions in 2! ways.
  the no. of favourable cases is (n-2)! 2 ! =6 ! 2 !
  
  P(seat together)= 6! 2 ! / 7!
  =6! 2!/ 7 .6 !
  =2!/7 =2/7
  P(never seat together)=1- (2/7)
  =(7-2) / 7
  =5/7
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