Chapter 8.5, Problem 42E

To determine

To find: the number of different batting orders can a baseball coach create from a team of 15 players by choosing nine players.

Answer to Problem 42E

There are 1816214400 possible ways.

Explanation of Solution

Given information:

Number of players in total 15.

Number of payer to be chosen is 9.

Calculation:

To select 9 players out of 15 players use permutation as order of the players to batting, is also required. So,

  $\begin{array}{c}{}_n{P}_x=\frac{n!}{\left(n-x\right)!}\\ {}_{15}{P}_9=\frac{15!}{\left(15-9\right)!}\\ =\frac{15\cdot 14\cdot 13\cdot 12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6!}{6!}\\ =1816214400\end{array}$

So, there are 1816214400 possible ways.