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

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.

As you can see, it is getting close to 1000 but never equals to 1000. ... no square roots of 1000 or one number (integer or whole number) that can be squared to make 1000. ... 1000 ft.2 is already an area, so it is also possible.

2 answers

Step-by-step explanation:

this should help you