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  4. PARAGRAPH A There are five students S1, S2, S3, S4 and S5 in a music class and for them there are five seats R1, R2,R3,R4 and R5 arranged in a row, where initially the seat Ri is allotted to the student Si, i=1,2,3,4,5. But, on the examination day, the five students are randomly allotted the five seats. Question:The probability that, on the examination day, the student S1 gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her is

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Q. 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 the five seats.
Question: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

JEE AdvancedJEE Advanced 2018

Solution:

Required probability $=\frac{4 !\left(\frac{1}{2 !}-\frac{1}{3 !}+\frac{1}{4 !}\right)}{5 !}$
$=\frac{9}{120}=\frac{3}{40}$