Five(5) men and five(5) women patricipate in a contest. They are classified according to their performance and two people cannot take the same place.Obviously,there are 10! combinations of rankings. Let X be the the highest rank taken by a woman (for example, X=1 if a woman took the first position, we have X=6 if the five women ranked in the last positions). Find the mass distribution function of X.
I thought that range is Sx=(1,2,3,4,5) and that Px(x)=P(X=x)= Sx / 10!. Is that correct? If yes can you help me determine Sx? If not can you tell me what methodology should I follow?