examday

/TMUA

A hockey team consists of $1$ goalkeeper, $4$ defenders, $4$ midfielders and $2$ forwards. There are $4$ substitutes: $1$ goalkeeper, $1$ defender, $1$ midfielder and $1$ forward. A substitute may only replace a player of the same category (e.g., midfielder for midfielder). Given that a maximum of $3$ substitutes may be used and that there are still $11$ players on the pitch at the end, how many different teams could finish the game?