1. Five men and 5 women are ranked according to their scores on an examination.

Assume that no two scores are alike and all 10! possible rankings are equally likely.

Let X denote the highest ranking achieved by a woman (for instance, X = 2 if the top-ranked person was male and the next-ranked person was female). Find P{X = i}, i = 1, 2, 3, . . . , 8, 9, 10.