ABSTRACT

In the previous chapters we have enumerated permutations according to various statistics. A similar line of research is to choose an n-permutation p at random, and compute the probability of the event that p has a given property A. Throughout this chapter, when we say that we select an n-permutation at random, we mean that each of the n! permutations of length n are chosen with probability 1/n!. Theoretically speaking, this is not a totally new approach. Indeed, the

probability of success (that is, the event that p has property A) is defined as the number of favorable outcomes of our random choice divided by the number of all outcomes. In other words, this is the number of n-permutations having property A divided by the number of all n-permutations, which is, of course, n!. Therefore, the task of computing the probability that p has property A is reduced to the task of enumerating n-permutations that have property p. The formal definition of discrete probability that we are going to use in this

book is as follows.