Question

In hockey, 6 players from each team are on the ice at a time: 1 goalie, 2 defence men, and 3 forwards.

A school hockey team has a total of 17 players: 2 goalies, 6 defensive players, and 9 forwards.

A) How many of these starting line ups include Sam, one of the team's goalies?

B) if the 2 goalies on the team are sick and cannot play, the coach will need to pick one of the defensive players to put in for the goalie. How many possible line ups are there now?

*****The answers to these questions should have something with combinations.

Please help. thanks.

Answer 1

a) since the goalie is picked, you still need 2 out of the 6 defensemen --> C(6,2)
and then 3 of the 9 forwards ----> C(9,3)
so no. of lineups = 1xC(6,2)xC(9,3)
= (15)(84) = 1260

b) Choose a goalie from the 6 defensemen
= C(6,1)

now choose 3 defensemen from the reamining 5
= C5,3)
and the 3 forwards from 9
= C(9,3)

so 6(10)(84) = 5040

Answer 2

oh ok, that makes sense. thanks