Latest TCS Aptitude Question SOLUTION: 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.

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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.

Asked In TCS arnavyagnik (10 years ago)

Solved janardhan Read Solution (10)

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Read Solution (10) :

janardhan  (10 years ago)

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

Is this solution Helpfull? Yes (46) | No (3)  

Gaurav Sharma  (10 years ago)

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!

Is this solution Helpfull? Yes (3) | No (1)  

RAVI VERMA  (10 years ago)

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

Is this solution Helpfull? Yes (3) | No (2)  

Geet Gobind Singh  (10 years ago)

(2*18*17!)/20! = (1/190)

Is this solution Helpfull? Yes (2) | No (3)  

Pooja  (10 years ago)

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

Is this solution Helpfull? Yes | No (3)  

RAVI VERMA  (10 years ago)

19!*380 ans

Is this solution Helpfull? Yes | No (5)  

RAVI VERMA  (10 years ago)

17!*18! is it the ans

Is this solution Helpfull? Yes | No (3)  

manaswini devabhakthuni  (10 years ago)

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!

Is this solution Helpfull? Yes | No (2)  

amruta patil  (8 years ago)

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

Is this solution Helpfull? Yes | No   

Mary Sheela jangam  (5 years ago)

18!*2 is ans

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