Question

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?

Answer 1

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:  $6! = 6*5*4*3*2*1=720$