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(#M40033478) TCS Numerical Ability question Keep an EYE

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

Asked In TCS Sruthi karuturi (10 years ago)

Unsolved Read Solution (21)

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Read Solution (21) :

ab  (10 years ago)

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

Is this solution Helpfull? Yes (90) | No (11)  

Dikshit  (10 years ago)

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)....

Is this solution Helpfull? Yes (28) | No (9)  

srishti singh  (10 years ago)

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

Is this solution Helpfull? Yes (20) | No (7)  

sanju  (10 years ago)

I think answer is 17!*2

Is this solution Helpfull? Yes (9) | No (18)  

gaurav anand  (9 years ago)

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

Is this solution Helpfull? Yes (8) | No   

Himanshu Soni  (10 years ago)

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

Is this solution Helpfull? Yes (4) | No (5)  

Anshul Chaurasia  (6 years ago)

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.

Is this solution Helpfull? Yes (4) | No   

sanju  (10 years ago)

plz giv me the correct solution

Is this solution Helpfull? Yes (2) | No   

Jasmeet  (10 years ago)

c is the correct ans

Is this solution Helpfull? Yes (2) | No (4)  

NAMRATA KASHYAP  (10 years ago)

18!*2 ways as the men can sit in 18! wayds and the two girls in 2! ways

Is this solution Helpfull? Yes (1) | No (6)  

bala bruce  (10 years ago)

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!

Is this solution Helpfull? Yes (1) | No   

karpagam  (9 years ago)

please give correct solution

Is this solution Helpfull? Yes (1) | No   

SANTOSH MOHANTY  (8 years ago)

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! )

Is this solution Helpfull? Yes (1) | No   

bharti garg  (7 years ago)

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

Is this solution Helpfull? Yes (1) | No   

Anindya Mallick  (9 years ago)

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..

Is this solution Helpfull? Yes | No (4)  

Abhishek Das  (8 years ago)

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.

Is this solution Helpfull? Yes | No (2)  

Valeti Sai Thulasi  (6 years ago)

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

Is this solution Helpfull? Yes | No   

Shankar  (6 years ago)

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

Is this solution Helpfull? Yes | No   

Sahil Hada  (5 years ago)

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!

Is this solution Helpfull? Yes | No   

sai kumar kotha  (5 years ago)

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

Is this solution Helpfull? Yes | No   

BHAVANI S  (5 years ago)

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

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