Question

Twelve girls try out for the hockey team. Two play goal, four play defence, and the rest play forward. How many different starting lineups could the coach choose if she needs 1 goalie, 2 defence, and 3 forwards?

Answer 1

There are 2 choices for 1 goalie, 4C2 possible combinations for the 2 defence and 6C3 combinations for the 3 forward. Therefore the total number of different lineups is found from:
$2\times4C2\times6C3=240$
There are 240 possible different lineups.