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Probability Level 5

There are 5 students S1,S2,S3,S4,S5S_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 TiT_i denote the event that SiS_i and Si+1S_{i+1} do NOT sit adjacent to each other on examination day. (i=1,2,3,4)

What is the probability that T1,T2,T3,T4T_1,T_2,T_3,T_4 all occur simultaneously on examination day?

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

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