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#1 2006-07-12 11:47:51

MathsIsFun
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Combinations and Permutations

I have just finished a rough draft of Combinations and Permutations.

I may have mistooks, so feel free to tell me smile


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#2 2006-07-12 17:57:32

Patrick
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Re: Combinations and Permutations

2. Combinations without Repetations
...
then adjustment so the order does not matter.


I dont get that line?


edit: I must be tired... I guess it should just be "adjust"?

Last edited by Patrick (2006-07-12 17:58:50)


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#3 2006-07-12 19:05:52

justlookingforthemoment
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Re: Combinations and Permutations

That was fun. I want some ice cream now.

A lonely, sad mistook that I came across:
How many variations will there be. (?)

That's all. smile

 

#4 2006-07-19 07:37:58

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Re: Combinations and Permutations

Patrick wrote:

then adjustment so the order does not matter.

Thanks, made it: "then alter it so the order does not matter"

And I added the "?" jl smile


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#5 2006-07-28 15:27:40

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Re: Combinations and Permutations

Page slightly updated (notation and reference to Pascal's Triangle).

I have also made a new page Combinations and Permutations Calculator

I have a special feature: different wordings of the question, so that you can hopefully relate the mathematics to real world problems. If you can improve the wording or think of new wordings please feel free to tell me.

Also please check if it gives the right answers!


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#6 2006-07-29 16:10:12

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Re: Combinations and Permutations

I have been brave and included a "List" facility in the calculator. It took me a while, but I *think* it works correctly.

Could someone please check that I have the right lists? for Comb/Perm, with/without repetition.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#7 2011-12-05 17:25:35

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Re: Combinations and Permutations

I have been working on a new version!

Here is its (temporary) location: Combinations and Permutations Calculator TEST VERSION

I would very much appreciate if everyone could give it a good work out and report back any bugs or suggestions smile


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#8 2011-12-05 18:20:56

bobbym
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Re: Combinations and Permutations

Hi MIF;

That is a lot to cover so I am only at the beginning. For combinations with repetition and order is not important. For this example,

{c,l,v} to choose 3 from the 3 the output is

{c,c,c} {c,c,l} {c,c,v} {c,l,l} {c,l,v} {c,v,v} {l,l,l} {l,l,v} {l,v,v} {v,v,v} 

which is correct.

When you enter a,a,b,c and attempt to pick 2 from that 4 you get:

{a,a} {a,a} {a,b} {a,c} {a,a} {a,b} {a,c} {b,b} {b,c} {c,c}

Why are there duplicates like {a,a}?

I believe the answer is



For the case of repeated elements in the input such as a,a,b,c in which you only draw a few is complicated.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#9 2011-12-05 21:05:09

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Re: Combinations and Permutations

Eeee ... hadn't thought about that.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#10 2011-12-06 22:52:34

bobbym
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Re: Combinations and Permutations

Hi;

Everything else is checking out okay. Keep the list feature.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#11 2011-12-07 08:21:58

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Re: Combinations and Permutations

Thanks bobby.

Repeated elements are, I think, too complicated for this app, so I might just check for them then warn user / remove them.

However there is scope for some future app where we could put in "rules" for combinations (like seating arrangements etc). What say you?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#12 2011-12-07 08:30:03

bobbym
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Re: Combinations and Permutations

Hi;

Combinatorics and probability are the hardest things in mathematics. Even strong mathematicians can make mistakes in reasoning. Each problem pretty much demands a unique solution.

I thought that you were close to the answer on your app right now. What I did with the answer the app returned was sort each arrangement and then just eliminate duplicates.

Whether this approach would always work I can not say for sure.

I am forced to agree that my first reaction was to just stop the user from entering any duplicates as you suggest.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#13 2011-12-07 08:44:10

John E. Franklin
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Re: Combinations and Permutations

Nice app!
Combinations without repetition (n=10, r=4)
abcd abce abcf abcg abch abci abcj abde abdf abdg abdh abdi abdj abef abeg abeh abei abej abfg abfh abfi abfj abgh abgi abgj abhi abhj abij acde acdf acdg acdh acdi acdj acef aceg aceh acei acej acfg acfh acfi acfj acgh acgi acgj achi achj acij adef adeg adeh adei adej adfg adfh adfi adfj adgh adgi adgj adhi adhj adij aefg aefh aefi aefj aegh aegi aegj aehi aehj aeij afgh afgi afgj afhi afhj afij aghi aghj agij ahij bcde bcdf bcdg bcdh bcdi bcdj bcef bceg bceh bcei bcej bcfg bcfh bcfi bcfj bcgh bcgi bcgj bchi bchj bcij bdef bdeg bdeh bdei bdej bdfg bdfh bdfi bdfj bdgh bdgi bdgj bdhi bdhj bdij befg befh befi befj begh begi begj behi behj beij bfgh bfgi bfgj bfhi bfhj bfij bghi bghj bgij bhij cdef cdeg cdeh cdei cdej cdfg cdfh cdfi cdfj cdgh cdgi cdgj cdhi cdhj cdij cefg cefh cefi cefj cegh cegi cegj cehi cehj ceij cfgh cfgi cfgj cfhi cfhj cfij cghi cghj cgij chij defg defh defi defj degh degi degj dehi dehj deij dfgh dfgi dfgj dfhi dfhj dfij dghi dghj dgij dhij efgh efgi efgj efhi efhj efij eghi eghj egij ehij fghi fghj fgij fhij ghij

Last edited by John E. Franklin (2011-12-07 08:45:25)


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#14 2011-12-11 18:30:50

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Re: Combinations and Permutations

Thanks everyone.

I have now posted v2.01 to the main page.

It includes removing duplicates from the list. I added a "CSV" list option as well.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#15 2011-12-11 19:16:34

bobbym
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Re: Combinations and Permutations

Hi MIF;

I can not find it, can you post the link?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#16 2011-12-11 19:46:30

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Re: Combinations and Permutations

Combinations and Permutations Calculator

(Use refresh, you should see v2.01)


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#17 2011-12-11 20:10:45

bobbym
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Re: Combinations and Permutations

Hi MIF;

This is what I am getting. When I view larger I get the old version!


Uploaded Images
View Image: Screenshot - 12_11_2011 , 1_06_01 AM.gif      


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#18 2011-12-12 08:08:37

MathsIsFun
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Re: Combinations and Permutations

Really? Just a blank?

What version of Flash Player do you have?

Does anyone else have the same problem?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#19 2011-12-12 08:14:08

bobbym
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Re: Combinations and Permutations

Hi;

10.0.12.36 which is a little old. I will be updating today to version 11. That might do it. I will let you know.

Working fine now. Nice new features. Thanks!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

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