The varsity soccer team has 30 players. Three of the players are trained to be goalies and the remaining 17 players can play any position. Only 11 players may be on the field at the same time. a) We want to find the number of possible groups of 11 players the coach can choose. Is this a permutation or combination? WHY?

b) If the coach wanted to choose 11 starters at random by drawing names from a hat, how many possible groups of 11 starters could the coach choose?

c) The coach want to make sure there is exactly one goalie on the field. How many ways can the coach choose a lineup of 11 players if exactly 1-player must be a goalie?