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There are six students S₁, S₂, S₃, S₄, S₅ and S₆ and for them there are six seats R₁, R₂ , R₃, R₄, R₅ and R₆ arranged in a row, where the initially seat R_i is allotted to the students S_i, i=1,2,3,4,5,6 . But on a day all are allotted seats randomly.

Options

  1. AThe probability that S₄ gets allotted, seat R₄ and none of the remaining students gets the seat previously all
  2. BThe probability that S₅ gets allotted seat R₅ and none of the remaining gets the seat previously allotted to t
  3. CThe probability that even numbered of students are seating at even numbered seat and none of the students is s
  4. DThe probability that even numbered of students are seating at even numbered seat and none of the students is s

Correct answer

C. The probability that even numbered of students are seating at even numbered seat and none of the students is s

Step-by-step solution

(1) and (2) probability = 1 D₅ 6 ! = 44 720 = 11 180 aligned & (3) and (4) Dearrangement of S₂, S₄, S₆ at R₂, R₄, R₆=D₃=2 & Dearrangement of S₁, S₃, S₅ at R₁, R₃, R₅=D₃=2 & probability = 2 2 6 ! = 1 180 & aligned

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