Consider ordering n people (distinguishable objects) around a table which can be arbitrarily ‘rotated’.

(a) If n > 4 people are randomly seated around a table, what is the probability that persons A and B sit next to one another?

(b) If n > 4 people are randomly seated around a table, what is the probability that persons A and B sit next to one another, and persons C and D sit next to one another?

(c) If two boys (B) and two girls (G) randomly sit at a table (with four chairs), what is the probability that they alternate, i.e. as in Figure 3.8? What do you think of the ‘solution’: because the only possibilities are the two shown in Figure 3.8, the probability is 1/2?

(d) If n boys and n girls randomly sit at a table (with 2n chairs), what is the probability that they alternate?

G B G B G B B G