Distinct degree factorizations for polynomials over a finite field

Let Fq[X] denote the multiplicative semigroup of monic polynomials in one indeterminate X, over a finite field Fq . We determine for each fixed q and fixed n the probability that a polynomial of degree n in Fq[X] has irreducible factors of distinct degrees only. These results are of relevance to various polynomial factorization algorithms.