How many ways can the manager of a baseball team make up the batting order, assuming the pitcher bats last?
To determine the number of ways the manager of a baseball team can make up the batting order, assuming the pitcher bats last, we need to consider the number of choices available for each position in the lineup.
In a typical baseball lineup, there are nine positions, including the pitcher. However, since we are assuming the pitcher bats last, we only need to consider the remaining eight positions.
For the first position in the lineup, the manager has eight choices to select any of the remaining eight players.
For the second position in the lineup, the manager has seven choices remaining since one player has already been chosen for the first position.
For the third position, there are six choices left, and this reduction by one choice continues for each subsequent position until the eighth position, where there are only two choices.
For the final position, the pitcher automatically fills it since we assumed the pitcher bats last.
To find the total number of ways to make up the batting order, we need to multiply these choices together. This can be done using the factorial function (!) denoted as n!, which represents the product of all positive integers less than or equal to n.
So, the number of ways to make up the batting order can be calculated as 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320.
Therefore, the manager of a baseball team can make up the batting order in 40,320 different ways, assuming the pitcher bats last.