A Probability distributions in an ordered set of extracted elements

[jazzy]

TL;DR

Finding the probability distributions in an ordered set of random extracted elements

Hello, I tried looking for an existing solution for the following problem:
"Assume that S is a set of d elements, and R is a total order relation on S. Assume that n elements are randomly extracted from S, and then they are ordered according to R. Which is the probability that in the i-th position of the ordered set of n elements there is the x-th element of S? (where the x-th element of S is intended according to the R).

In other words, which is the probability distribution function for the i-th position of the ordered set of n elements? Do you know whether such problem has already been solved? I did not find any specific solution in literature or elsewhere. I tried do find my own solution, but I would like to know if something already exist.

 

[mathman]

Try Mathematics Stack Exchange https://math.stackexchange.com/

 

[Office_Shredder]

I don't think this is that hard. To get the xth element of R in the ith position, you need to pick x-1 elements smaller than it, and n-x-1 elements larger than it. You can just count the number of ways to do this. Why don't you give it a shot?