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Question:

For i=1,2,3,4, let Ti denote the event that the students Si and Si+1 do NOT sit adjacent to each other on the day of the examination. Then the probability of the event T1∩T2∩T3∩T4 is?

110

760

15

115

Solution:

n(T1∩T2∩T3∩T4) = Total - n(¬T1∪¬T2∪¬T3∪¬T4) = 5! - (⁴C₁4!2! - (³C₁3!2! + ³C₁3!2!2!) + (²C₁2!2! + ⁴C₁2⋅2!)) = 14
Probability = 14/5! = 14/120 = 7/60