how many batting lineups of the nine players can be made for a baseball team if the cathcher bats first, the shortstop second and the pitcher last?

Answer 1

If we leave out the catcher, the shortstop and the pitcher, that leaves us with 6 positions to fill.
There will be a choice of 6 people for the first of the 6 position, and 5 for the next, until the last there is one.
How many lineups can you make?

Answer 2

720!

Answer 3

We have then only 6 positions to play with:
6 * 5 * 4 * 3 * 2 * 1 = 6! = 720