Question

There are five students `S_(1),S_(2),S_(3),S_(4)` and `R_(5)` arranged in a row, where initially the seat `R_(1)`is allotted to the students are randomly allotted the five seats `R_(1),R_(2),R_(3),R_(4)` and `R_(6)` arranged in a row, where initially the seat `R_(i)` is allotted to the student `S_(i)i,=1,2,3,4,5. But, on the examination day, the five students are randomly allotted the five seats.
(There are two questions based on Paragraph, the question given below is one of them)
The probability that, on the examination day, the student `S_(1)` gets the previously allotted seat `R_(1)`, and NONE of the remaining students gets the seat previously allotted to him/her is
A. `(3)/(40)`
B. `(1)/(8)`
C. `(7)/(40)`
D. `(1)/(5)`

Answer 1

Correct Answer - A
Here five students `S_(1),S_(2),S_(3),S_(4) and S_(5)` and five seats `R_(1),R_(2),R_(3),R_(4) and R_(5)`
`:.` Total number of arrangement of sitting five students is `5!=120` .
Here , `S_(1)` gets previously alloted seat `R_(1)` .
`:. S_(2) ,S_(3),S_(4) and S_(5)` not get previously seats .
Total number of way `S_(2) , S_(3), S_(4) and S_(5)` not get previously seat is
`4! (1- (1)/(1!) +(1)/(2!) -(1)/(3!) +(1)/(4!))=24(1-1+(1)/(2)-(1)/(6)+(1)/(24))=24((12-4+1)/(24))=9`
`:.` Required probability `=(9)/(!20)=(3)/(40)`