Q.There are 7 man and 5 women sitting in a circle, find the all possible way so that two women wont sit together?

• 7 men can sit in a circle in (7-1)!= 6! ways
  no two women sit together,so woman have to sit alternate to men
  there will be 7 places,in which 5 women have to sit
  so women can sit in 7 places as 7P5 ways
  reqd ways= 6!*7P5
  
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• 10 years agoHelpfull: Yes(21) No(1)
• 7 man can sit in circle in (7-1)! ways
  there are 7 places between 7 man
  we have to sit 5 women in between them
  no of ways selecting the 5 places out of 7 places = 7c5
  no of arrangement for women= 7c5*5!
  now,
  total no of arrangement= 7c5*5!*(7-1)!
  = 7c5*5!*6!
  = 7p5*6!
• 10 years agoHelpfull: Yes(11) No(0)
• In a round table, 7 men can sit in 6! ways because a round table has no start and end points, so 1_2_3_4_5_6_7_ is similar to 7_1_2_3_4_5_6_.
  Now there are 7 empty spaces that can be filled by 5 women...so as this is a process of arrangement we use permutation, so its 7P5
  
  So 6! * 7P5
• 9 years agoHelpfull: Yes(1) No(0)