Instructions

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 54

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 $$𝑇_{1} \cap 𝑇_{2} \cap 𝑇_{3} \cap 𝑇_{4}$$ is

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