In a music class, five students labeled S1, S2, S3, S4, and S5 are assigned five seats labeled R1, R2, R3, R4, and R5 in a row, where each student Si initially sits in seat Ri (i = 1, 2, 3, 4, 5). On exam day, the students are seated randomly in the five seats. Define Ti as the event where

Question

In a music class, five students labeled S1, S2, S3, S4, and S5 are assigned five seats labeled R1, R2, R3, R4, and R5 in a row, where each student Si initially sits in seat Ri (i = 1, 2, 3, 4, 5). On exam day, the students are seated randomly in the five seats. Define Ti as the event where students Si and Si+1 do NOT sit next to each other for i = 1, 2, 3, 4. What is the probability of the event T1 ∩ T2 ∩ T3 ∩ T4?

Accepted Answer

7/60. The probability of the event T₁ ∩ T₂ ∩ T₃ ∩ T₄ is 7/60, which can be determined by analyzing the possible seating arrangements that satisfy the given conditions and then calculating the probability based on these arrangements.

Solution

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