Question

A starting lineup in a soccer game consists of 11 players. A certain team uses two formations. Formation 1 consists of 1 Goalkeeper, 4 Defenders, 3 Midfielders and 3 Forwards. Formation 2 consists of 1 Goalkeeper, 3 Defenders, 5 Midfielders and 2 Forwards.

This team has on its roster 3 Goalkeepers, 8 Defenders, 6 Midfielders, and 5 Forwards.

a) In Formation 1, how many different starting lineups can be created?

b) In Formation 2, how many different starting lineups can be created?

Answer 1

a) Number of different starting lineups that can be created is computed here as:

= Number of ways to select 1 goalkeeper from 3 goalkeepers * Number of ways to select 4 defenders from 8 defenders * Number of ways to select 3 midfielders from 6 midfielders * Number of ways to select 3 forwards from 5 forwards

b) Number of different starting lineups that can be created is computed here as:

= Number of ways to select 1 goalkeeper from 3 goalkeepers * Number of ways to select 3 defenders from 8 defenders * Number of ways to select 5 midfielders from 6 midfielders * Number of ways to select 2 forwards from 5 forwards