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There are five students `S_(1), S_(2), S_(3), S_(4)` and `S_(5)` in a music class and for them there are five seats `R_(1), R_(2), R_(3), R_(4)` and `R_(5)` 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.
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)`

Text Solution

Verified by Experts

The correct Answer is:
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)`
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