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Question

The Benton Youth Soccer Team has 20 players on the team, including reserves. Of these, three are goalies. Today, the team is having a contest to see which goalie can block the most number of penalty kicks. For each penalty kick, a goalie stands in the net while the rest of the team (including other goalies) takes a shot on goal, one at a time, attempting to place the ball in the net.

How many penalty kicks must be taken to ensure that everyone has gone up against each of the goalies?

Accepted Answer

For each of the 3 goalies who stand in the net, there are 19 other players who will kick to the goalie. That makes 3 19 = 57 penalty kicks that must be taken.