Solve the problem

A baseball manager has 11 players. How many 9 players starting lineups can he create?

1 answer

To solve this problem, we can use the combination formula, which is given by:

C(n, r) = n! / (r!(n-r)!)

In this case, the manager has 11 players (n=11) and needs to select 9 players for the starting lineup (r=9). Therefore, the number of 9 player starting lineups that the manager can create is:

C(11, 9) = 11! / (9!(11-9)!)
= 11! / (9!2!)
= (11 * 10 * 9!) / (9! * 2)
= (11 * 10) / 2
= 110 / 2
= 55

Therefore, the baseball manager can create 55 different 9 player starting lineups.