Probability problem

[Genevie]

commuters leaving a train station can exit through any one of three turnstiles, a, b, or c. assuming that a commuter is equally likely to select any one of the three turnstiles, what is the probability that among four commuters, two select gate a, and at least one selects gate c?

 

[Deleted member 4993]

commuters leaving a train station can exit through any one of three turnstiles, a, b, or c. assuming that a commuter is equally likely to select any one of the three turnstiles, what is the probability that among four commuters, two select gate a, and at least one selects gate c?

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[Genevie]

 

[pka]

commuters leaving a train station can exit through any one of three turnstiles, a, b, or c. assuming that a commuter is equally likely to select any one of the three turnstiles, what is the probability that among four commuters, two select gate a, and at least one selects gate c?

This question is about occupancy. It is not about individuals.
Suppose that you were doing a survey for the transit authority. At a particular exit there three gates for four people.The company cares not who uses the gates just how many. There are a total of \(\dbinom{4+3-1}{4}\) number of ways for four to exit using three gates.
How many ways are there for two to use gate A and at least one to use gate C. I get two ways: \(AABC~\&~AACC\)