Instructions

There are five students $$๐‘†_{1}, ๐‘†_{2}, ๐‘†_{3}, ๐‘†_{4} and ๐‘†_{5}$$ in a music class and for them there are five seats $$๐‘…_{1}, ๐‘…_{2}, ๐‘…_{3}, ๐‘…_{4} and ๐‘…_{5}$$ arranged in a row, where initially the seat $$๐‘…_{๐‘–}$$ is allotted to the student $$๐‘†_{๐‘–}$$, ๐‘– = 1, 2, 3, 4, 5. But, on the examination day, the five
students are randomly allotted the five seats

Question 54

For ๐‘– = 1, 2, 3, 4, let $$๐‘‡_{๐‘–}$$ denote the event that the students $$๐‘†_{๐‘–}$$ and $$๐‘†_{๐‘–}$$+1 do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event $$๐‘‡_{1} \cap ๐‘‡_{2} \cap ๐‘‡_{3} \cap ๐‘‡_{4}$$ is


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