At a math summer camp, there were three participants from New York and three participants from California. The six students were paired up into teams of two. One participant noticed that in each pair there was one student from New York and one from California and asked, "What is the probability of this happening at random?" Answer the student's question.
At another camp, nine students (three from New York, three from California, and three from Missouri) are divided into teams of three and each team has one representative from each state. What is the probability of this happening?
Source: Ivy Fitzgerald