Question

There are eleven people on a softball team and nine different positions. Work through the questions to determine how many ways a coach can choose the players for the positions if Amy does not want to pitch.

If there are eleven people on the team and nine positions, how many total arrangements of the players can be made?

If Amy does not want to play pitcher, then there are now
people available to pitch.

Assuming the pitcher has already been chosen, there are ten remaining players and
remaining positions. How many ways are there to arrange the remaining players and positions?

Answer 1

- Total arrangements (11 people, 9 distinct positions): P(11,9) = 11! / 2! = 19,958,400.

- If Amy refuses to pitch, there are 10 people available to pitch.

- After the pitcher is chosen, there are 10 remaining players and 8 remaining positions. The number of ways to arrange them is P(10,8) = 10! / 2! = 1,814,400.

(For the full count with Amy not pitching: 10 choices for pitcher × 1,814,400 = 18,144,000.)