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## Homework Statement

5 men and 5 women are ranked according to exam scores. Assume no two scores are the same and each 10! rankings are equally likely. Let random variable X denote the highest ranking achieved by a woman e.g. X=2 means the highest test score was achieved by 1 of the 5 men and the second highest by 1 of the 5 women. Find P{X=i}, i=1,2,3,...,10.

## Homework Equations

## The Attempt at a Solution

I am quite lost on this problem, I have a very poor background in statistics so I'm not sure if there is a specific formula I should be using or what the most efficient way of doing this is, but P{X=i}, i=7,8,9,10 is 0 because there are only 5 men so the lowest a woman can be ranked is 6th place. I think P(X=1) = 5* 9!/10!, P(X=2)=5*8!/10!, P(X=3)=5*7!/10!, P(X=4)=5*6!/10!, P(X=5)=5*5!/10! and P(X=6)=5*4!/10! since there are 5*9! different rankings (9! combinations times 5 different possible women ranked at that position) with a woman ranked first and so on. So is P(X=i), i=1,2,...,10 the summation of these probabilities or P(X=i)=.567 (assuming they are correct)?

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