Question 641952
You have 3 slots locked up because "the center fielder must bat fourth, the second baseman must bat third and the pitcher last". So you have 9 - 3 = 6 players to arrange in 6 slots.


There are 6! = 6*5*4*3*2*1 = 720 different ways to arrange the 6 remaining players. So there are 720 different lineups.