assuming X people sit down around a (round) table, Y people have black shirts and X-Y people have white shirts, what is the probability that the two clusters of shirts are grouped together (i.e., all the black shirts sit together, all white shirts together) around the table?
i've thought about this using standard permutations with circular probability (i.e., (X p Y) / (X-1)!). i've also thought about it sequentially (i.e., someone with a black shirt sits down, so looking at the probability that another black shirt sits down, and another, etc). i get similar results with both methods but do not believe either approach is correct.
thanks in advance for the help and sorry to bore with rudimentary math.