How many batting lineups of the nine players can bemade for a baseball team if the catcher bats first, the

shortstop second, and the pitcher last?

To determine the number of batting lineups, we can consider the remaining six positions in the lineup. These six positions can be filled by the six players who are not the catcher, shortstop, or pitcher.

We can approach this problem by using the concept of permutations. In this case, we have six players remaining, which means there are six possible choices for the first position in the batting lineup. After selecting a player for the first position, there will be five players remaining for the second position, and so on.

Using this logic, the number of batting lineups can be calculated as follows:

6 choices for the first position × 5 choices for the second position × 4 choices for the third position × 3 choices for the fourth position × 2 choices for the fifth position × 1 choice for the sixth position

Therefore, the number of batting lineups is 6 × 5 × 4 × 3 × 2 × 1 = 720.

So, there are 720 different batting lineups that can be made for the baseball team under the given conditions.

six players, in six positions?

6!