Question

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?

Answer 1

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:

$P_{(n,x)} = \frac{n!}{(n-x)!)}$

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

$P_{15,9} = \frac{15!}{(15-9)!} = \frac{15!}{6!} = 1816214400$

1,816,214,400 batting orders are possible.