Question

The varsity soccer team has 20 players. Three of the players are trained to be goalies while the remaining 17 can play any position. Only 11 players can be on the field at once. The coach wants 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

Answer 1

Answer:

The coach can choose a lineup of 11 players in 6,047,981,701,347 different ways.

Step-by-step explanation:

Since the varsity soccer team has 20 players, and three of the players are trained to be goalies while the remaining 17 can play any position, and only 11 players can be on the field at once, and the coach wants to make sure there is exactly one goalie on the field, to determine how many ways can the coach choose a lineup of 11 players if exactly 1 player must be a goalie the following calculation has to be made:  

3 x 17 ^ 10 = X

3 x 2,015,993,900,449 = X

6,047,981,701,347 = X

Therefore, the coach can choose a lineup of 11 players in 6,047,981,701,347 different ways.