Associated Topics || Dr. Math Home || Search Dr. Math

Baseball Batting Orders

```
Date: 10/14/2001 at 18:27:28
From: Erica
Subject: Word problem!

How many possible batting orders are there for a team of nine players?

```

```
Date: 10/15/2001 at 15:19:12
From: Doctor Ian
Subject: Re: Word problem!

Hi Erica,

Often when a problem seems too big to tackle, you can make some
progress by considering a smaller problem.

Suppose there is only 1 player (a). Then there is only 1 possible
order, right?

a

What if we add a second player (b)? He could go either before or after
a, right?

a -> ba
ab

So there are two possible orders for two players. What if we add a
third player (c)? He could go in any position in any of the orders we

a -> ba -> cba
bca
bac
ab -> cab
acb
abc

So now we have 1*2*3 different orders. Let's try it for one more
player (d):

a -> ba -> cba -> dcba
cdba
cbda
bca -> dbca
bdca
bcda
bac -> [4 more orders]
ab -> cab -> [4 more orders]
acb -> [4 more orders]
abc -> [4 more orders]

Now we have 1*2*3*4 different orders.

It looks as if when we add the n'th player, we multiply the number of
possible orders by n (because there are n possible changes to each of
the orders we had before). So if we keep going until we have 9
players, how many possible orders would we have?

Does this help?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Permutations and Combinations

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search