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 January 29th, 2017, 07:44 AM #1 Senior Member   Joined: Jan 2016 From: Blackpool Posts: 104 Thanks: 2 Help on Combinatorics Hey guys I am struggling to understand what the difference is between ordered and unordered selection between a set of elements. Could anyone please give me an example which i might find helpful to understand them? Thanks again and sorry for the spam!
January 29th, 2017, 08:42 AM   #2
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 Originally Posted by Jaket1 Hey guys I am struggling to understand what the difference is between ordered and unordered selection between a set of elements. Could anyone please give me an example which i might find helpful to understand them? Thanks again and sorry for the spam!
Consider selecting colored balls from an urn as in your other problem.

The set will be ordered if I care about which color was selected first, which was selected second, etc.

In this case, $\{B, B, G\}$ is considered a distinct event from $\{G, B, B\}$

On the other hand if we only care about what balls we end up with after all the selections are made we have an unordered selection.

In this case the two color triples above are considered the same event.

Last edited by romsek; January 29th, 2017 at 09:36 AM.

January 29th, 2017, 05:07 PM   #3
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 Originally Posted by Jaket1 Hey guys I am struggling to understand what the difference is between ordered and unordered selection between a set of elements. Could anyone please give me an example which i might find helpful to understand them? Thanks again and sorry for the spam!
Suppose we have three people Al (A), Bob (B), and Chuck (C). Now consider the set of people $\displaystyle \{A,B,C\}$.

1. Suppose we want to know how many committees of size 2 can be formed. There are 3. They are AB, AC, and BC. Notice that if the committee is Al and Bob, then Bob and Al is the same committee.

2. Suppose we want to know how many president, vice-president pairs there are. There are 6. They are AB, BA, AC, CA, BC, CB. Notice that president Al and vice-president Bob is different than president Bob and vice-president Al.

The first problem is called a combination. The second is called a permutation.

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