Math Is Fun Forum
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#26 2014-09-15 01:44:26
Re: Permutation Problems
How do I get the coefficient of x^4 from that gf without using a CAS?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#27 2014-09-15 01:48:56
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Permutation Problems
One way is by simple arithmetic, everybody knows how to multiply a polynomial.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#28 2014-09-15 01:56:54
Re: Permutation Problems
That will take too much time.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#29 2014-09-15 02:02:26
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Permutation Problems
Not if you expand intelligently. Should take about 10 - 15 minutes.
Or you can treat this like a series and do the coefficients that way. Both ways are tedious. The questions you are asking are a whole course on gf's.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#30 2014-09-15 02:05:11
Re: Permutation Problems
How can I take those courses?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#31 2014-09-15 02:10:15
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Permutation Problems
Combinatorics is one of the most difficult parts of math. Much harder than analysis or calculus. Most people will not even attempt to solve a combinatorics problem.
Give me the time and I will answer the question but it will not be quick.
I will teach you but you will have to do it my way.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#32 2014-09-15 02:25:27
Re: Permutation Problems
Okay, teach me.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#33 2014-09-15 02:29:29
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Permutation Problems
That will take a long time too. You will learn gradually by doing with a minimum of theory. You will start by getting two books online, the Tucker book I talk about all the time and Generatingfunctionology by the great mathematician Herbert S. Wilf, the best.
Want to see the casework answer?
1 pair:
2 pairs:
All the same:
Just 2, {k, k, k, k} and {c, c, c, c}
3 of the same:
36 + 18 + 2 + 24 = 80
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#34 2014-09-15 02:59:36
Re: Permutation Problems
Would you please explain the casework? I do not get what you mean by 1 pair and etc
I have never seen you talking about Tucker and gfology is very hard unless I have a good foundation of gf's.
Last edited by Agnishom (2014-09-15 03:02:37)
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#35 2014-09-15 03:01:56
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Permutation Problems
The first chapter helps a lot of people learn about gf's. Do not think, read as far as you can get.
The Tucker book I recommend to everyone who asks for a book. I sat on my bed and started reading it. A couple of months later I could do combinatorics.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#36 2014-09-15 03:04:17
Re: Permutation Problems
Would you please explain the casework? I do not get what you mean by 1 pair and etc
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#37 2014-09-15 03:05:55
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Permutation Problems
For 1 pair:
s = Permutations[{k, k, k, k, k, c, c, c, c, t, t, t}, {4}];
Select[s, Length[Union[#]] == 3 &]
%//Length
run that and look at them.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#38 2014-09-15 04:07:16
Re: Permutation Problems
Yes, but how did you get that expression?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#39 2014-09-15 04:10:03
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Permutation Problems
How many pairs are possible?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#40 2014-09-15 04:11:39
Re: Permutation Problems
A pair of kabooblydoos, a pair of transparent soaps and a pair of carrots.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#41 2014-09-15 04:15:44
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Permutation Problems
3 is correct and after the pair is chosen how many different singles are there?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#42 2014-09-15 04:35:31
Re: Permutation Problems
binomial(3,2) or simply 3
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#43 2014-09-15 04:40:43
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Permutation Problems
You have 2 types left after you choose the pair, for instance you choose kk, now you have c and t to make the reamining two. Obviously that can be done in only 1 way or
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#44 2014-09-15 04:43:53
Re: Permutation Problems
Oh, sorry. Now I multiply 4! In the denominator to get all the possible arrangements and divide by 2! Because there is one repeatition.
Please explain me the two pairs.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#45 2014-09-15 04:45:40
Re: Permutation Problems
For two pairs, you have two select the two kinds whose pairs are taken. There are binomial(3,2) ways to do that and then with the same reasoning you multiply with 4! An divide with 2! And 2!
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#46 2014-09-15 04:46:15
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Permutation Problems
Take a look at them:
s2 = DeleteCases[Select[s, Length[Union[#]] == 2 &], {___, a_, ___, a_, ___, a_, ___}]
Length[s2]
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
#47 2014-09-15 04:49:40
Re: Permutation Problems
What does the regex mean?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#48 2014-09-15 04:51:56
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Permutation Problems
One thing at a time, your froggy characteristics are showing.
Did you look at the lists and the number of them?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#49 2014-09-15 04:58:52
Re: Permutation Problems
It is 18 but what is wrong with post 45?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#50 2014-09-15 05:02:52
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Permutation Problems
Double posting carries with it the seeds of confusion.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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