How many batting lineups are there for nine players of a baseball team if the center fielder must bat fourth, the second baseman must bat third and the pitcher last?

The number of possible batting lineups is 720

Explanation

Total number of players in the team = 9

The center fielder must bat fourth, the second baseman must bat third and the pitcher last. That means, 3 slots in the batting line-up are already assigned to 3 players.

So, the remaining (9 - 3) = 6 players will be assigned to remaining 6 slots.

Thus, the possible number of ways so that 6 players can be assigned to 6 slots will be: