Math Is Fun Forum
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#1 2013-12-28 15:25:50
Simple Combinatorics Problem
In how many ways can a committee of 5 members be selected from 10 aspirants provided that the youngest is excluded when the oldest is included?
'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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#2 2013-12-28 15:33:23
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
Hi;
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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#3 2013-12-28 15:44:01
Re: Simple Combinatorics Problem
That is the correct answer but Explain
'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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#4 2013-12-28 16:02:52
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
You should program this to see if it is right.
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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#5 2013-12-28 16:28:56
Re: Simple Combinatorics Problem
Why 8 c 3?
I am not sure how to program it
'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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#6 2013-12-28 19:50:19
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Simple Combinatorics Problem
"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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#7 2013-12-28 22:01:39
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
Hi gAr;
Yep!
Hi Agnishom;
Why 8 c 3?
That is the number of committees that have the youngest and the oldest.
Do you know how to program to count combinations?
Here is the old fashioned way to do the problem.
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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#8 2013-12-29 15:34:42
Re: Simple Combinatorics Problem
I see.
What does the gf solution 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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#9 2013-12-29 19:42:40
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
Hi;
This might be a little easier to understand
where o is the oldest, y is the youngest and p are other people. That says how many combinations that we can make when we pick 10 people that consist of 3 types.
When you expand that you get:
Since we want 5 people, we check all the pertinent terms whose powers add up to 5 and have either no oldest-youngest or one of each.
Notice I left out,
why?
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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#10 2013-12-30 02:47:53
Re: Simple Combinatorics Problem
Because it contains both o and y!
Now, how do I make a gf for a random problem like this?
'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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#11 2013-12-30 03:00:03
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
In schools they teach the magic of the binomial approach first. This is a mistake. It is difficult for most students to grasp the concept. It sure was for me. The generating function approach is more natural because it only depends on polynomial multiplication, something all algebra students are exposed to early.
To formulate a gf you only have to practice. But since you are in school and subject to the way they do things I suggest in order to get good grades that you do the NCR first.
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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#12 2013-12-30 03:03:34
Re: Simple Combinatorics Problem
I think I know the NcR as much as I shuld
'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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#13 2013-12-30 03:05:30
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
Want to do a problem or 2 using a gf approach?
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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#14 2013-12-30 03:10:02
Re: Simple Combinatorics Problem
indeed.
'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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#15 2013-12-30 03:20:32
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
Let's look at the one we did up there already. We got for an answer,
If the powers represent what the groups are.
For instance,
70 o p^4
means this is a group of 4 people and the oldest person. What does the 70 mean?
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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#16 2013-12-30 03:47:18
Re: Simple Combinatorics Problem
It means the number of possible people containining the old and 4 people
'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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#17 2013-12-30 03:52:01
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
It means there are 70 ways for that to happen. So, the powers say what the group is and the coefficients tell us how many of that group.
There is a nice relationship between diophantine linear equations and gfs. This is the link between number theory and combinatorics. But where number theory is concerned with what the solutions are, combinatorics is concerned with how many there are.
Let's do one more easy one.
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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#18 2013-12-30 04:00:15
Re: Simple Combinatorics Problem
Okay;
'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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#19 2013-12-30 04:09:12
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
That is the gf that represents a single die. The exponents keep track of the faces ( 1 to 6 ).
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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#20 2013-12-30 04:12:55
Re: Simple Combinatorics Problem
Why does it not have a 1+ ? Is it because there is no 0?
'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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#21 2013-12-30 04:15:34
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
Is there a 0 face?
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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#22 2013-12-30 04:16:31
Re: Simple Combinatorics Problem
No. There isn't. Do the powers mean something?
'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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#23 2013-12-30 04:19:12
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
The powers are the faces. Supposing you had a 5 sided die with the numbers 1,3,5,7,9 on the faces. What would the gf be?
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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#24 2013-12-30 04:21:27
Re: Simple Combinatorics Problem
I read somewhere that the x is just there to carry the powers around
'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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#25 2013-12-30 04:41:01
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Simple Combinatorics Problem
That is very good!
Now for the question. How many ways can I get a sum of 20 if I threw a standard die 4 times?
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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