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?
21. Ans: 2250 .
$\binom{3}{1} \times\binom{ 5}{2} \times\binom{ 5}{4}$ choices for goalkeepers, strikers and midfielders respectively. The remaining midfielder and defenders can all play as defenders, hence total number of possibilities are
$$
3 \times 10 \times 5 \times\binom{ 6}{4}=2250 \text {. }
$$