PARAGRAPH A 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 five seats. (For Ques. No. 17 and 18) 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 `3/(40)` (b) `1/8` (c) `7/(40)` (d) `1/5`

Options

A. `(3)/(40)`
B. `(1)/(8)`
C. `(7)/(40)`
D. `(1)/(5)`

Answer

A

Explanation

Total number of cases = `5!`
Since `S_(1)` gets seat `R_(1)` and none of the other gets previously allotted seat, we have derangement of 4 students. So, required probability
`=(4!(1-(1)/(1!)+(1)/(2!)-(1)/(3!)+(1)/(4!)))/(5!) = (9)/(120) = (3)/(40)`