I thought this was a probability question since it would most likely be solved using a Combination or Permutation, but could not find a sub-forum for that, so here I am on this particular sub-forum. This isn't really help on homework or anything, just a question I came up with on my own and couldn't figure out the answer to.

So in my fantasy baseball league, there are 12 coaches. Each coach drafts 23 players (9 pitchers, 5 Outfielders, 1 1B, 1 2B, 1 SS, 1 3B, 1 middle infielder (SS or 2B), 1 corner infielder (3B or 1B), 2 catchers, and a utility hitter (any position).

There are 30 teams in the MLB to choose players from, and each team has 25 players to choose from, making a total of 750 players to choose from (I don't want to include minor league players in this problem).

Each team has a different number of positional (some have more pitchers than hitters, or more outfielders than infielders etc) and some players are eligible for more than one position (if they played more than 20 games in that position the previous year, then they are eligible for that position).

What I want to solve for is the number of possible drafts that can happen, assuming a snake draft (coaches pick players 1-12 then 12-1 then back to 1-12 etc.). I don't even really want a solution for any given year, but more an equation that would let me solve it for any given year. Is it even possible to write one equation that would solve it for any year?