# Double selection with varying size selection set (beginner)

I'm self-taught in statistics, so I have some holes in my knowledge for sure. please bear with me.

I have a hard time defining my problem. I want to figure out if my selection procedure (governed by hardware) produces a flat, or close enough to flat probability mass function that I can work on the resulting data as if it was uniformly distributed.

from a limited set of data (my sample space $$S_A$$) I select a random data entity, containing some items, I call this $$S_B$$. I use random selection for this (uniform), so $$P(A)=1/N_A$$.

In $$S_B$$ I select $$m$$ random items, for $$B\choose m$$ combinations. In my project I do work on these random items. The catch is that $$S_B$$ contains some elements that cannot be changed, and the elements that cannot be changed are not distributed evenly. So I believe that $$m$$ changes.

But maybe the problem can be represented as the intersection of all the probabilities $$P\left(A\cap B\cap C^{\prime}\right)$$ where $$P(A)=1/N_A$$, $$P(B)=1/{B\choose m}$$, and $$P(C)$$ is the average chance of an element of $$S_B$$ being "changeable". $$P(C^\prime) = 1 - P(C)$$

But still, I'm expecting to be corrected here. I do this selection millions of times to build up statistics on the effects of the change, and also correlate the changes with $$S_A$$

Just to be clear, $$S_B$$ is a subset of $$S_A$$. And the probability I believe I need is the probability that a random element has been changed. What I wish for is that this probability is uniform, or close to it over $$S_A$$.

The problems I see, are that $$P(C)$$ is a function in $$S_A$$. So I'm not really confident in this.

Thanks for any input.