Random Multinomial Variable Nine persons go into a 3-carriage tram. Each person chooses the carriage at random. Which are the probabilities of the event: A : “There are 4 person in a carriage, 3 in another, and 2 in the other one”? The answer should be $\frac{280}{729}$

Answer to your question is $$\frac{\frac {9!}{4!3!2!}}{3^9}=0.0640146...$$