Answer:
1,816,214,400 batting orders are possible.
Step-by-step explanation:
The order is important.
Suppose we had a two player batting order.
A batting order of Jonathan Schoop and Manny Machado is a different order than Manny Machado and Jonathan Schoop. So we use the permutations formula.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!)}[/tex]
A baseball coach is creating a nine-player batting order by selecting from a team of 15 players. How many different batting orders are possible?
Selection of 9 players from a set of 15 players. So
[tex]P_{15,9} = \frac{15!}{(15-9)!} = \frac{15!}{6!} = 1816214400[/tex]
1,816,214,400 batting orders are possible.
