20 people with two sisters among them want to sit around a round table such that the two sisters are exactly separated by one person sitting in between them. Find the probability.

• 20 people in which 2 sisters are there and the condition is that 2 sisters should be seperated by 1 person
  (s1 p s2) be 1 set
  then 20-3 persons => 17 persons + 1 set= 18
  18 can be arranged in 17! ways bcz it is circular permutuation
  the 2 sis can be arranged in 2! ways
  and the p place can be filled in 18 ways
  and the total permutations are 19!
  probability is = (2!*18*17!)/(19!)
  = 2/19
• 9 years agoHelpfull: Yes(46) No(3)
• 1 person between two sister can be grouped as 1 person so left with 17person
  total 18 person
  18 person can be arranged in 18!
  and Sister person sister can be arranged only in 2 ways
  So ans is 2!*18!
• 9 years agoHelpfull: Yes(3) No(1)
• 17! to arrange 18 people around the table and 18p2to arrange two girls in the 18 spaces by the 18 people
  so ans is
  17!*18*17/(19!)=17/19
  
  
• 9 years agoHelpfull: Yes(3) No(2)
• (2*18*17!)/20! = (1/190)
• 9 years agoHelpfull: Yes(2) No(3)
• we consider (Sister1-Person-sister2) as a one object.
  so they can be arranged in (20-1)!*2*20C1=19!*40
  so probability=(19!*40)/21!=2/21
• 9 years agoHelpfull: Yes(0) No(3)
• 19!*380 ans
  
• 9 years agoHelpfull: Yes(0) No(5)
• 17!*18! is it the ans
  
• 9 years agoHelpfull: Yes(0) No(3)
• consider 3 people 2 sisters and in middle one person..these 3 and the remaining 17 can be arranged in 18!ways..and the middle person is choosen in 18 ways..the two sisters are exchanged among themselves in 2 ways..hence...2*18*18!=36*18!
• 9 years agoHelpfull: Yes(0) No(2)
• Taking the 2 sisters, they can be placed in 2! ways
  *The person between them can be 1 among 18 i.e. 18 ways
  *The 17 people between them other way around can be seated among themselves in 17! ways
  *Taking circular table implies clockwise and anti clockwise symmetry reduces the possible chances by half
  
  So in all the number of permutations available such that "20 people with two sisters among them to sit around a round table such that the two sisters are exactly separated by one person sitting in between them" is
  
  (2!)*(18)*(17!)*(1/2) ways
  
  2!=2*1=2
  cancelling 2! and (1/2) leaves 18*17! which is 18! ways
  
  Total cases (19!)/2
  therefore the probability is
  (18!)/((19!)/2) = (2*(18!))/(19*(18!)) = 2/19
• 7 years agoHelpfull: Yes(0) No(0)
• 18!*2 is ans
• 4 years agoHelpfull: Yes(0) No(0)