Hopefully I'm posting this to the appropriate section. I am trying to figure out a formula for describing the number of possible answer "paths" that may be taken by an individual who is administered a filtered test format. In the filtered test format, the individual must select a passing response to item j in order to proceed to item j + 1. If the individual selects a failing option, the test is over. My question is, given that each of the items on the test can have different numbers of passing and failing options (e.g., item j might have two passing options and three failing options, item j + 1 might have one passing option and two failing options), how can I even begin to figure out how to put this down mathematically on paper? My math background is rather weak, so I'm not really even sure where to start. Any help would be much appreciated!