Question

a softball coach is creating the starting lineup of three batters for the next game how many different ways can three batters be selected for the starting lineup is 14 players are on the softball team.

Answer 1

There are 14 players on the softball team, we don't care about the order but we can't repeat a player. So we are going to use combinations, we don't care in what order the players are placed - we only care that they are in the batting order somewhere.

c = n! / (x! *( n -x))

Where n = 14 and x=3

Replace and solve

c = 14! / (3! * ( 14 -3)!)

c = 14! / (3! * ( 14 -3)!) = 364 ways