In how many ways can eight people comprising four married couples sit at a circular table such that no two men sit together and no husband sits beside his wife?

1) 8
2) 2
3) 16
4) 12

• 2*3! ways,
  
  Let husbands be A,B,C & D, and their wives be 1,2,3,4 respectively.
  
  Now let us place husbands in alternative positions, for fulfilling second requirement,
  
  A_B_C_D_
  
  Being circular problem the blank after D is actually between A&D
  
  Now according to first condition following options can fill the blanks in order,
  
  3,4
  
  4,1
  
  1,2
  
  2,3
  
  But now there is one more twist, that not all the possible combinations from this set can work for example if we choose 3 for first blank, then 1 for second and, 2 for third then we cannot fill the last position.
  
  So, if we choose 3 for first position, then we have to choose 4 for second, 1 for third and 2 for forth.
  
  Same holds for choosing 4 for first position.
  
  Now we can position husbands in 3! position in a circular table.
  
  So total number of ways are 2*3! = 12
• 5 years agoHelpfull: Yes(0) No(0)