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← JEE Advanced 2018 · Paper 1
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JEE Advanced 2018 · Paper 1, Mathematics question 17

Passage

There are five students S1,S2,S3,S4S_1, S_2, S_3, S_4 and S5S_5 in a music class and for them there are five seats R1,R2,R3,R4R_1, R_2, R_3, R_4 and R5R_5 arranged in a row, where initially the seat RiR_i is allotted to the student SiS_i, i=1,2,3,4,5i = 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 S1S_1 gets the previously allotted seat R1R_1, and NONE of the remaining students gets the seat previously allotted to him/her is

Choose one option
Answer and worked solution

Official answer: A

S1S_1 must sit in R1R_1 and the other four must all be displaced. That is a derangement of 4:
D4=4!(1−1+12−16+124)=9.D_4=4!\left(1-1+\frac12-\frac16+\frac1{24}\right)=9.

Probability.
95!=9120=340.\frac9{5!}=\frac9{120}=\frac3{40}.

(A)