Market maker for events with more than one winning outcome


I wonder if we can build a market maker for events with a defined number of winning outcomes. Lets say we want to predict the players that will start in a soccer game. Lets say the team has 20 players and we know exactly 11 will start.

We could do: a) 20 markets for each player whether or not he will play. However - in this case all markets would be independent although they are not. We can also make the "brute force" solution where we have all possible combinations of 11 players. However - this might get messy.Is there a market maker algorithm for n outcomes with a k winners?

By the way - maybe the "brute force" solution is better because I guess you lose the ability to express that it is unlikely that player A and player B will player together in the other solution.

However - all possible outcomes can become unfeasible so such a market maker will be useful anyway.