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#1 2014-04-03 23:03:10

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Probability-1


A pack of forty cards numbered 1-10 and four suits are well shuffled and placed face up on the floor.
After placing the cards sequentially, the positions are numbered like this
[1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5]
A card numbered 1 must not occupy a position numbered 1, and same restriction for cards 2-7. Cards 8-10 are free to be placed anywhere.
What's the probability of such an arrangement?

Last edited by gAr (2014-04-05 01:02:10)


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#2 2014-04-04 05:06:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: Probability-1

Hi;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2014-04-04 05:50:48

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

Hi,


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#4 2014-04-04 15:07:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: Probability-1

Hi;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#5 2014-04-04 17:07:00

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

Hi,


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#6 2014-04-05 00:48:04

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Probability-1

Hi gAr

Shouldn't the positions be numbered 1,2,3,4,5,6,7,0,1,2,…?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#7 2014-04-05 00:59:18

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

Mmm, yes. I wanted to tell 1+ (pos# mod 7), I overlooked it.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#8 2014-04-05 01:01:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: Probability-1

Hi;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#9 2014-04-05 01:03:23

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Probability-1

gAr wrote:

Mmm, yes. I wanted to tell 1+ (pos# mod 7), I overlooked it.

Ah, okay then. I wasn't sure which definition to hold true. Thanks for the clarification.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#10 2014-04-05 01:10:36

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

Hi bobbym,


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#11 2014-04-05 01:15:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: Probability-1

Hi gAr;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#12 2014-04-05 01:16:29

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

Ah, okay then. I wasn't sure which definition to hold true. Thanks for the clarification.

You're welcome.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#13 2014-04-05 01:18:28

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

Hi bobbym,


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#14 2014-04-05 06:11:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: Probability-1

Hi gAr;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#15 2014-04-05 06:24:30

ShivamS
Member
Registered: 2011-02-07
Posts: 3,557

Re: Probability-1

Why don't you use a simulation first? I am getting

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#16 2014-04-05 06:29:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: Probability-1

Hi ShivamS;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#17 2014-04-05 06:49:42

ShivamS
Member
Registered: 2011-02-07
Posts: 3,557

Re: Probability-1

Close, but still wrong... I think my algorithm is correct, but I probably made a mistake in my code.

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#18 2014-04-05 07:43:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: Probability-1

Hi;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#19 2014-04-05 07:45:18

ShivamS
Member
Registered: 2011-02-07
Posts: 3,557

Re: Probability-1

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#20 2014-04-05 08:04:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: Probability-1

Hi;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#21 2014-04-05 08:06:11

ShivamS
Member
Registered: 2011-02-07
Posts: 3,557

Re: Probability-1

Great! Now time to find some algebraic method.

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#22 2014-04-05 15:17:32

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

Hi ShivamS,

Hi bobbym,


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#23 2014-04-05 15:51:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: Probability-1

Hi gAr;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#24 2014-04-05 16:02:00

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

Hi bobbym,


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#25 2014-04-05 16:44:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: Probability-1

Hi;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

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