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#1 2013-01-07 12:21:18

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

probability

In how many ways can we distribute 13 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving an equal number of pieces?


I see you have graph paper.
You must be plotting something
lol

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#2 2013-01-07 12:39:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: probability

I would say 308.


“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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#3 2013-01-07 12:48:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: probability

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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#4 2013-01-07 12:55:28

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: probability

From bobbym's Diophantine equation in the post above we can form the GF:

Last edited by anonimnystefy (2013-01-08 05:08:17)


“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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#5 2013-01-07 12:56:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: probability

Hmmm, but do ye have the diophantine equation?


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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#6 2013-01-07 12:58:32

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: probability

Hi bobbym

I was still editing when you posted. See the post again.

Last edited by anonimnystefy (2013-01-07 12:59:49)


“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 2013-01-07 13:00:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: probability

Hi;

So where is the diophantine equation?

Oh sorry, you peeked and I did not see.


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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#8 2013-01-07 13:04:20

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: probability

I am refering to your diophantine in the post just above.


“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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#9 2013-01-07 13:10:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: probability

Yes, I see that.

How about the recurrence:

with a(0)=1,a(1)=3


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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#10 2013-01-08 00:49:42

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: probability

I think that I can even get a closed form for the terms...


“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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#11 2013-01-08 04:18:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: probability

Hi;

That may be a little bit more difficult than it appears for the same reason why that recurrence is false!


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 2013-01-08 04:51:22

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: probability

Got it!


“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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#13 2013-01-08 04:56:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: probability

Hi;

You did not read post #11, that is not quite correct.


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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#14 2013-01-08 04:59:44

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: probability

I did read it, but I do not see what is wrong...


“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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#15 2013-01-08 05:03:40

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: probability

Supposing I asked you to use that formula for 50 pieces of candy would you get the right answer?


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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#16 2013-01-08 05:07:18

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: probability

I am getting 12051.


“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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#17 2013-01-08 05:11:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: probability

Yes, that is correct.

I meant coming up with an analytical form for the coeffs of the expansion of the polynomial in post #3. But I guess that is not really that important.


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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#18 2013-01-08 05:14:29

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: probability

So my formula in post #9 is correct?


“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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#19 2013-01-08 05:21:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: probability

Hi;

Yes, I believe it is. I got,


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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#20 2013-01-08 05:42:17

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: probability

I think the two are same... I just put mine in the form above because of the common expression 1+(-1)^n. It is noce to know that that part is 0 when n is odd.


“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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#21 2013-01-08 05:43:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: probability

Hi;

I know how I got mine, may I ask how you got yours?


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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#22 2013-01-08 05:45:54

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: probability

Partial fractions, then expanding.


“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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#23 2013-01-08 05:55:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: probability

Hi;

Did them by maxima?


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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#24 2013-01-08 06:42:42

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: probability

Partial fractions in Maxima and expanding by hand.


“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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#25 2013-01-08 06:53:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: probability

Hi;

Okay, somehow though I do not think these answers are what the OP will require.


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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