I'm building a neural network for data analysis, however I'm stuck on how many output neurons I need and what they should represent. The neural network tries to predict peoples choices for certain objects. There are 75 possible objects, but here's the catch, they choose 6 of them at a time. These six can (theoretically, though this won't happen realistically) be any combination of the 75 objects, in rare cases there might even be duplicates of a certain object in this set of six.
I naturally considered creating an output neuron for each possible set, but since that would lead to 75^6th output neurons (or more if we consider duplicates) I imagine that that would have disadvantages for the learning speed. Another option I considered is just taking the six highest ratest items as a set, but I'm unsure if this would work since the choice of the second, third, etc. objects depend on which earlier objects were chosen. I wonder if there are any better, faster or more accurate ways of doing this?
Edit, some more information about the trainingdata: The neural network will be used to analyse the ingame item choices in the computergame called league of legends. There players can choose up to six items each game. These six items are most likely based on some factors that change each game such as the ingame characters they and their enemies play, but also things such as what the other 5 items are they have. However, the reason for this may be universal to all games. For instance, the (likely) biggest reason why items depend on eachother is the multiplicativity of item stats, if you already have an item that makes your attacks hit harder then getting an item that allows you to attack more often is going to do more for you than getting an item that makes your attacks hit even harder. There are also some links between item choices though, while probably more limited, there is for instance an item that returns damage to the enemy when he attacks you, while it's not detrimental it is probably not a great idea to combine that with an item that lowers the amount of attacks that an enemy can do to you.