So there is a system (it's actually from a videogame but I will just explain it in simple words) where you need to perform 30 attempts in a row of getting a success with a certain probability. It works like this - you press the button and there is a probability that this attempt is going to be successful. The two possible outcomes are: success or failure and it is recorded (you do 30 of them in a row and each one is recorded and the resulting chain of success\failed cases is what you get at the end). The probability for the next attempt goes up if the current one fails, or down if the current one succeeds.
There are a few details though, the 30 attempts are split between 3 rows (the effects that you are rolling on, 2 positive that you want to succeed as much as possible on, and 1 negative that you want to fail every time ideally, 10 attempts per each row, you can hit them in any order but 10 per row max).
What I am interested in is how many different ways there are to arrive at a certain combination of all the factors, meaning how many different ways could I have arranged my choices made and results recorded for each attempt before the current one, say by the time I am on my final 30th attempt.
The answer does not have to be a precise number at all, my only goal is to see if the number is huge or not (say I'm trying to memorize all these combinations, is it realistic for a human?). For example, how would the number compare to 1 million?
Can I look at this problem as the "number of permutations" problem? (Roughly speaking).
