Chapter 13.2, Problem 59AYU

Baseball Teams A baseball team has 15 members. Four of the players are pitchers, and the remaining 11 members can play any position. How many different teams of 9 players can be formed?

To determine

To find: How many batting orders is it possible for a manager to use?

Answer to Problem 59AYU

There are 660 possible batting orders.

Explanation of Solution

Given:

A baseball team has 15 members. Four of the players are pitchers, and the remaining 11 members can play any position. How many different teams of 9 players can be formed?

Formula used:

$C\left(n,r\right)=\frac{n!}{r!\left(n-r\right)!}$

Calculation:

The team must have a position for a pitcher and remaining 8 positions for non pitcher.

Hence,

Number of choices for the pitcher is $C\left(4,1\right)$.

Number of choices for the remaining 8 players is $C\left(11,8\right)$.

Hence, the number of different team possible is $C\left(4,1\right)*C\left(11,8\right)$.

$=\frac{4!}{1!*3!}*\frac{11!}{8!*3!}$

$=4*\frac{11*10*9}{3*2}$

$=4*165$

$=660$

There are 660 possible batting orders.