JEE Advanced 2018 — Paper 1 — Question 48

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.

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