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

Options

A. `(1)/(15)`
B. `(1)/(10)`
C. `(7)/(60)`
D. `(1)/(5)`

Answer

C

Explanation

Event `T_(1)nn T_(2) nn T_(3) nn T_(4)`: No two students with consecutive index sit adjacent.
So, we have following possible arrangements:
13524, 14253
24135, 24153, 25314
31425, 31524, 35142, 35241
41352, 42531, 42513
52413, 53142 ltgtbrgt Thus, favorable cases = 14
Hence, required probability = `(14)/(120) = (7)/(60)`