There are n randomly placed books on a shell with the two-volume edition of Jack London among them. Suppose that the different book arrangements are equiprobable. What is the probability that both volumes are located near each other?
There are n! possible ways to arrange n books on the shell. Two books together (Vol.1, Vol.2) can be placed among these n books in (n-1) different ways (Vol.1 takes places 1..(n-1), Vol.2 takes places 2..n). According to the task, the order doesn’t matter ((Vol.1, Vol.2)~(Vol.2, Vol.1), they just have to be placed together), then there are 2*(n-1) different ways to do that. Thus, the probability that both volumes are located near each other is: P = 2*(n-1)/n!