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JEE Advanced 2018Paper 1
Exam
JEE Advanced
Year
2018
Paper
Paper 1
Subject
Mathematics
Chapter
Probability

JEE Advanced 2018 · Paper 1 · Mathematics · Probability

Paragraph: There are five students S _ 1 , S _ 2 , S _ 3 , S _ 4...

Paragraph: There are five students S1,S2,S3,S4{S}_{1}, {S}_{2}, {S}_{3}, {S}_{4} and S5{S}_{5} in a music class and for them there are five seats R1,R2,R3,R4{R}_{1}, {R}_{2}, {R}_{3}, {R}_{4} and R5{R}_{5} arranged in a row, where initially the seat Ri{R}_{i} is allotted to the student Si,i=1,2,3,4,5.{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 S1{S}_{1} gets the previously allotted seat R1,{R}_{1}, and NONE of the remaining students gets the seat previously allotted to him/her is

Options

  1. A340\dfrac{3}{40}
  2. B18\dfrac{1}{8}
  3. C740\dfrac{7}{40}
  4. D15\dfrac{1}{5}

Correct answer

A. 340\dfrac{3}{40}

Step-by-step solution

Required probability =4!(12!−13!+14!)5!=9120=340= \dfrac{4 ! \left(\dfrac{1}{2 !} - \dfrac{1}{3 !} + \dfrac{1}{4 !}\right)}{5 !} = \dfrac{9}{120} = \dfrac{3}{40}
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