# Thread: random variable equal class rank of 10 with 5 men and 5 women

1. ## random variable equal class rank of 10 with 5 men and 5 women

There are 5 men and 5 women in a class. X is the ranking of the top ranked woman in the class, where 1 is the highest ranking and 10 is the lowest. The question asks what is the probability that X equals each ranking from 1-10. I can clearly see that for 7-10 the answer is 0 simply because of the amount of people not adding up, but I have no idea even where to start with the rest of the answers. I want to say that any other position is just 1/2 but I feel like there's more to it than that. Can anyone help me?

2. ## Re: random variable equal class rank of 10 with 5 men and 5 women

Originally Posted by tzvidf
There are 5 men and 5 women in a class. X is the ranking of the top ranked woman in the class, where 1 is the highest ranking and 10 is the lowest. The question asks what is the probability that X equals each ranking from 1-10. I can clearly see that for 7-10 the answer is 0 simply because of the amount of people not adding up, but I have no idea even where to start with the rest of the answers. I want to say that any other position is just 1/2 but I feel like there's more to it than that. Can anyone help me?
We can rank order this class in 252 ways with respect to sex alone.
In other words, we can ignore identity of the people.
Then $\displaystyle \mathcal{P}(X=k)=\frac{\binom{10-k}{4}}{252},~k=1,2,\cdots,6$.