# Permutation or Combination

• December 5th 2009, 11:00 AM
skeske1234
Permutation or Combination
A baseball team has 13 members. If a batting line-up consists of 9 players, how many different batting line-ups are possible?

The answer in my textbook for this question uses permutations to derive the answer.. However, I believe that it's wrong.. you should be using combinations to find the answer. I think combinations because in this question, its asking for a line-up of batting players.. in this case, order doesn't matter.. Does it?

Also, just another side question:
if a question is talking about a sports team.. would it be a permutation or combination? I think it's combinations for sports teams.. but then this question with the baseball team makes me think otherwise.. But what's really right? should it be combinations or permutations for any sports team q?
• December 5th 2009, 11:32 AM
Hello skeske1234
Quote:

Originally Posted by skeske1234
A baseball team has 13 members. If a batting line-up consists of 9 players, how many different batting line-ups are possible?

The answer in my textbook for this question uses permutations to derive the answer.. However, I believe that it's wrong.. you should be using combinations to find the answer. I think combinations because in this question, its asking for a line-up of batting players.. in this case, order doesn't matter.. Does it?

Also, just another side question:
if a question is talking about a sports team.. would it be a permutation or combination? I think it's combinations for sports teams.. but then this question with the baseball team makes me think otherwise.. But what's really right? should it be combinations or permutations for any sports team q?

Being a Brit, I don't know for sure what is meant by a 'batting line-up' for a baseball match. But in any event, the key question is: Does the 'line-up' change when the same 9 players are arranged in a different order? or is it the same line-up? If it does change, then it's a permutation that you want; if it doesn't, it's a combination.

I suspect that a permutation is what is required here. On the other hand, if you have to select a squad of, say, 21 players from a pool of 28 available to travel abroad for a competition, then you'd use a combination, because at the selection stage it doesn't matter what order the players are in.

Only a detailed knowledge of the details of the problem will lead you to the correct answer; I can only give you the principles that you must work by.

• December 5th 2009, 01:55 PM
Soroban
[size=3]Hello, skeske1234!

Quote:

A baseball team has 13 members.
If a batting line-up consists of 9 players, how many different batting line-ups are possible?

The answer in my textbook for this question uses permutations to derive the answer.
However, I believe that it's wrong. You should be using combinations to find the answer.
I think combinations because in this question, its asking for a line-up of batting players.
In this case, order doesn't matter... Does it?

Well, of course, order matters!
Do you understand what a line-up is?

It looks like this:

. . $\boxed{\begin{array}{cc}1. &\text{Hoo bats first.} \\ 2.&\text{Watt bats second.} \\ 3. & \text{Idunno bats third.} \\ \vdots & \vdots\end{array} }$