Question 21
Your national football coach brought a squad of $18$ players to the $2010$ World Cup, consisting of $3$ goalkeepers, $5$ defenders, $5$ midfielders and $5$ strikers. Midfielders are versatile enough to play as both defenders and midfielders, while the other players can only play in their designated positions. How many possible teams of $1$ goalkeeper, $4$ defenders, $4$ midfielders and $2$ strikers can the coach field?