Question: A train has three coaches and when it stops at the first station during its journey, n passengers embark it, for n > 3. Assuming

A train has three coaches and when it stops at the first station during its journey, n passengers embark it, for n > 3. Assuming that passengers embark on a particular coach of the train independently of one another, what is the probability that at least one passenger embarks on each coach?

(Hint: Define the events Ai ∶ no passenger embarks the ith coach for i = 1, 2, 3, and express the event of interest in terms of A1, A2, A3.)

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