No copying, students.

Probability Level 5

There are 5 students $S_1,S_2,S_3,S_4,S_5$ in a music class and for them there are 5 seats in a row. On examination day, all five students are randomly allotted the five seats. Let $T_i$ denote the event that $S_i$ and $S_{i+1}$ do NOT sit adjacent to each other on examination day. (i=1,2,3,4)

What is the probability that $T_1,T_2,T_3,T_4$ all occur simultaneously on examination day?

If the probability is of the form $\dfrac {a}{b}$ , where $a$ and $b$ are coprime positive integers, find $a+b$