A family consisting of four persons—A, B, C, and D—belongs to a medical clinic that always has a doctor at each of stations 1, 2, and 3. During a certain week, each member of the family visits the clinic once and is assigned at random to a station. The experiment consists of recording the station number for each member. Suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned.
What is the probability that one station has two family members at it and the others have only one?
I have the answers and see multiple ways to get to the answer, but it might just be a coincidence or some relation I'm not seeing. I've tried binomial method but it wasn't consistent to get other answers. I just need a clear method for these type of problems.