Q36 / 54 · JEE Advanced 2018 (Paper 1) · Mathematics

Paragraph: 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 : For i = 1,2,3,4 Let T i denote the event that the students S i and S i+1 do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event T1∩ T2∩ T3∩T4 is

  • A
    115
  • B
    110
  • Correct answer
    C
    760
  • D
    15

Solution

nT1∩T2∩T3∩T4 =Total-nT1¯∪T2¯∪T3¯∪T4¯
=5!- 4C14!2!- 3C1.3!2!+ 3C13!2!2!+ 2C12!2!+ 4C1.2.2!-2
=  14
Probability =145!=760

Hence, the correct answer is option: 'C'.

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