A subject is selected for the next task if he is the 1st solver of the 1st room or the 2nd solver of the 2nd room or the 1st solver of the 3rd room or the 2nd solver of the last room. So, it constitutes something close to a ranked set sample for the next task.

I want to find out the probability that the subject having the 5th ordered solving time was the 1st solver of the 1st room or the 2nd solver of the 2nd room or the 1st solver of the 3rd room or the 2nd solver of the last room. That is, I want to find out the probability of the 5th ordered solver to be selected for the next task.

Now, for being selected for the next task he should be able to solve the problem and the room he belongs to should have at least the necessary number of solvers. Say, a subject was randomly assigned to room 4, solved the problem, but room 4 had only 1 solver, then he could not be selected for the next task. So, the probability for ordered subject i seems like,

P(i gets selected for the next task|i solves the problem, the room it falls into has at least necessary number of solvers).

The probability seems to me like P(A|B,C) where events B and C are independent. How do I accurately calculate the probability? It seems complicated.

Thanks in advance for any help!