N2014 P2 Q6

A team in a particular sport consists of \(1\) goalkeeper, \(4\) defenders, \(2\) midfielders and \(4\) attackers.

A certain club has \(3\) goalkeepers, \(8\) defenders, \(5\) midfielders and \(6\) attackers.

1. How many different teams can be formed by the club?[2]

One of the midfielders in the club is the brother of one of the attackers in the club.

2. How many different teams can be formed which include exactly one of the two brothers?[3]

The two brothers leave the club. The club manager decides that one of the remaining midfielders can play as either a midfielder or as a defender.

3. How many different teams can now be formed by the club?[3]