A squad of 20 players (3 goalkeepers and 17 outfield players) splits into two equal teams for a training match (with any unchosen players reduced to spectating). Each team must have exactly one goalkeeper, but otherwise the players are entirely interchangeable.
It is calculated that there are a little over 5 million distinct* ways to select the teams.
*(so, for instance, if it were three-a-side, ABC v DEF would be the same as FDE v BCA).
How many players on each team?