A group of twelve persons is to be seated around a circular table. There are only two women in the group. Find the probability that there are atleast three men between the two women.

• We can make a group of two women with 3men in between and consider it as 1. Then there will be 7 left. That would give 8 in circular arrangements we take (n-1)! so 7! And the arrangement of women and men internally would be 2! And 3! So the answer is 7!2!3!
• 6 years agoHelpfull: Yes(8) No(1)
• 2 women and three men as 1 unit ,then 12-5=7
  7 left + 1 unit=8
  circular arrangement=(8-1)!=7!
  2 women in 2!
  3 men in 3!
  finally,7!2!3!
• 6 years agoHelpfull: Yes(3) No(0)
• Regardless of how the two women are seated, there are the same number of possible arrangements for the 10 men in the remaining 10 seats (10! arrangements, in fact). So each of the possible relationships between the seats of the two women is equally probable.
  
  Thus, we can arbitrarily pick the position of one of the women and simply consider how many, of the 11 other seats, are far enough away that there are at least 3 men in between?
  
  There are 2 seats adjacent to the first woman (no men in between),
  2 seats one position further away (one man in between),
  2 seats one more position further away (two men in between),
  2 seats with 3 men in between (the shortest way; the other 7 men are around the other direction),
  2 seats with 4 men in between,
  and 1 seat with 5 men in between (in each direction).
  
  So 5 out of the 11 seats have at least 3 men between the two women in both directions around the table.
• 6 years agoHelpfull: Yes(1) No(1)
• One woman is seated, 11 seats left.
  reject 3 seats on either side of this woman, seats left for another woman to sit = 5 (12 - 3*2 - 1)
  probability = 5/11
• 6 years agoHelpfull: Yes(1) No(0)
• We can make a group of two women with 3men in between and consider it as 1. Then there will be 7 left. That would give 8! And the arrangement of women and men internally would be 2! And 3! So the answer is 8!2!3!
• 6 years agoHelpfull: Yes(0) No(0)
• All others imagining the question wrongly as linear arrangement.. But the arrangement is circular
  
  Just imagine 12 persons seated with the initial arrangement as in the first condition mentioned..
  thus let M be men and W be women ...Let the arrangement be 'W'MMM'W'MMMMMMM imagine the given series as circular.....by your imagination the last M is sitting with first 'W' its right..proceed now..
  Let the 2nd 'W' move clockwise to reach the st 'W' with 3M lag...there are 5 probabilities for single movement..without condiotion there 11 movements...thus
  5/11*11/12(probability of one complete revolution of a woman..
  thus the answer is 5/12
• 5 years agoHelpfull: Yes(0) No(0)