There are 20 persons sitting in a circle. In that, there are 18 men and 2 sisters. How many arrangements are possible, in which the two sisters are always separated by a man?
a. 18!*2
b. 17!
c. 17!*2
d. 12

• 18!*2 Consider 1 man along with two sisters as one group.. so they can be arranged in 17! ways as circular.. The one man in between the two sisters can be out of any 18 men.. so,17!*18.. and the two sisters can be arranged in 2 ways..so 18!*2
• 10 years agoHelpfull: Yes(90) No(11)
• there are 20 persons in total and two sisters are seperated by a man.
  Let M---> man S--> sister
  let us consider SMS as one unit
  so items left = 17+ 1(SMS)=18
  so these 18 items can be arranged in circular table in (n-1)! ways ie. 17!*2!(two sisters can be arranged in 2! ways)....
• 10 years agoHelpfull: Yes(28) No(9)
• consider the two sisters and a man together as 1 unit
  now total left person are 17
  and we will add the 1for two sisters and a man combination
  so total 18 people now they can be arranged in 18! ways
  ttwo sisters can be interchanged
  so answer will be 18!*2
• 10 years agoHelpfull: Yes(20) No(7)
• I think answer is 17!*2
• 10 years agoHelpfull: Yes(9) No(18)
• first 18 men can sit in circle in 17! ways.Now we have 18 places for sisters.First sister can take any of 18 places.Now as per condition,second sister can sit only at a difference of one man,So we have only 2 places left for second sister (S2,M,S1,M,S2) so ans is 17!*18C1*2 = 17!*18*2=18!*2
  So, option A
• 9 years agoHelpfull: Yes(8) No(0)
• 18 men and a group of two sisters
  total no. of groups=20-2+1=19
  then seating arrangements of 19 persons in a circle=(19-1)!=18!
  and there will be 2 ways in which group of sisters can sit
  so the ans is 18!*2
• 10 years agoHelpfull: Yes(4) No(5)
• Let's suppose "SMS" consider single unit. Then total people are 17men and 1 unit "SMS" i.e. = 18.
  Means you have to find that 18 persons sitting in a circle.
  means (18-1)! // -1 because its circle
  there is a possibility for interchanging position of sisters
  means 17!*2
  there is also a possibility for sitting 18 men in between sisters.
  means (18)*17!*(2)
  we can write (18)*17! as 18!
  So, the answer is 18!*2.
• 6 years agoHelpfull: Yes(4) No(0)
• plz giv me the correct solution
• 10 years agoHelpfull: Yes(2) No(0)
• c is the correct ans
• 10 years agoHelpfull: Yes(2) No(4)
• 18!*2 ways as the men can sit in 18! wayds and the two girls in 2! ways
• 10 years agoHelpfull: Yes(1) No(6)
• a man is seated between two sisters. hence there is 1 probability(CMC). then the remaining 17 men can be arranged in (17!) since it is a circle the answer is 17! . if it were a row it will be 17! * 2!.
  
  hence the answer is 17!
• 10 years agoHelpfull: Yes(1) No(0)
• please give correct solution
• 9 years agoHelpfull: Yes(1) No(0)
• If we consider the two sister and the person in between the brothers as a block, then there will 17 others and this block of three people to be arranged around a circle.
  
  The number of ways of arranging 18 objects around a circle is in 17! ways.
  
  Now the sister can be arranged on either side of the person who is in between the brothers in 2! ways.
  
  The person who sits in between the two brothers could be any of the 18 in the group and can be selected in 18 ways.
  
  Therefore, the total number of ways 18×17!×2= 2 × 18!..........................(18!= 18*17! )
• 8 years agoHelpfull: Yes(1) No(0)
• answer is 18! x 2
  it can be calculated as-
  we have to separate 2 sisters ,for this we make a group of 3, in which extreme positions are taken by sisters and in mid position one man is there. ways of doing this is - 2x18x1 = 36
  now considering this group as a single unit ,we have total 18 units ( 17 men and 1 group) which can be arranged in 17! x 36 i.e 2x18x17! = 18! x2
• 7 years agoHelpfull: Yes(1) No(0)
• take SMS as a unit..
  then remaining nmbr is 17..
  total nmbr taking SMS as a sngle1=18 as 17+1(SMS)..
  now 18 people can arrnge themselves in a circle in (18-1)!=17! way..
  and the 2two sisters arrnge themselves in 2!way..
  so total arrngmnts can be=17!*2!=17!*2..ans..option C..
• 9 years agoHelpfull: Yes(0) No(4)
• The answer is none of this as the men can sit in 18! factorial ways. Now the first woman has 18 spaces to chose from, after the first woman now the second woman has 17 spaces left from.. So the answer is 18!*18*7.
• 8 years agoHelpfull: Yes(0) No(2)
• Let the first sister name is A. Now she can sit any where in the 20 places (Symmetrical). Now her sister B can sit to her left or right in 2 ways. Now the remaining 18 persons can be sit in 18 places in 18! ways. Total = 18! * 2
• 6 years agoHelpfull: Yes(0) No(0)
• consider S->sister M->man
  SMS is considered as 1 entity
  remaining 17 men
  17+1=18
  these 18 entities can be arranged in 18! ways
  in SMS, the two sisters can be arranged in 2 different ways
  hence, the answer is 18!*2
• 6 years agoHelpfull: Yes(0) No(0)
• All options are wrong answer is 17*18!
  Take 2 sister as 1 group , now there are 19 total people so to arrange them it is 18!... but both sister can be interchange so it is 2*18! ... This is for 2 sisters seats beside but we have to find reverse of it so.... total possible combination with 20 people(19!) - 2*18! = 18!(19-2) = 17*18!
• 5 years agoHelpfull: Yes(0) No(0)
• ab18!*2 Consider 1 man along with two sisters as one group.. so they can be arranged in 17! ways as circular.. The one man in between the two sisters can be out of any 18 men.. so,17!*18.. and the two sisters can be arranged in 2 ways..so 18!*2
• 5 years agoHelpfull: Yes(0) No(0)
• i was quite confused reading all these.....for those who all having the same issues....try this link
  https://www.quora.com/There-are-20-persons-sitting-in-a-circle-In-that-there-are-18-men-and-2-sisters-How-many-arrangements-are-possible-in-which-the-two-sisters-are-always-separated-by-a-man-The-answer-is-18-but-how
• 5 years agoHelpfull: Yes(0) No(0)