Math Is Fun Forum

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

permutation and combination

Consider the set of eight vectors V={

}.
Three non-coplanarvectors can be chosen from V in

ways.Then p is?

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friendship is tan 90°.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: permutation and combination

You might want to check your question.

---

'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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: permutation and combination

hi Niharika,

Did you mean {-1,1} ?

I'll write vectors as rows (rather than columns) to save having to construct the right forms.

So a possible vector would be (1,-1,1)

So that gives you the 8 vectors.

Sketch a cube, centred on (0,0,0) with these 8 points as the corners.

And then I come 'unstuck' because every three that I select are coplanar.

Wait a mo.  I'm thinking these are coordinates, not vectors. 

Thinking ..................

Got it!  I think!

If you choose any two, say OA = (1,1,1) and OB = (-1,1,1) then these form the plane that goes through (0,0,0) as well.  The plane is OAB.

There are exactly 2 points chosen from the other 6, that are also in this plane.  They are C = (-1,-1,-1) and D = (1,-1,-1)

So with that choice for the first two points there are 4 non coplanar choices for the third.

So proceed like this:

How many choices for the first vector?

How many choices for the second ?

How many non coplanar choices for the third?

You may end up counting the same solutions more than once so reduce by division.

Bob

ps.  yes that worked

Last edited by Bob (2015-03-13 02:00:23)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: permutation and combination

thanks I got it too.

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friendship is tan 90°.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: permutation and combination

I do not get the notion of coplanar vectors.

---

'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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: permutation and combination

Vectors are coplanar if there is a plane they are all parallel to.

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“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
The knowledge of some things as a function of age is a delta function.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: permutation and combination

Parallel is for lines/rays.

When I see (5,6,7), I think of a point

---

'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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: permutation and combination

Two vectors can be parallel too.

I would have defined coplanar vectors like this:

Two vectors that lie in the same plane.

Stefy's definition comes to the same as you can always translate the vector until it does lie in the plane.

Two non-parallel vectors in a plane will form a basis for all vectors that lie in that plane.  If the vectors are a and b you can write any other vector in that plane as a linear combination thus:

In the question, any two vectors will always generate a plane unless they are parallel (eg.  OA and OC in my explanation above)

You can choose the third so that it is not in that plane provided you avoid the two vectors that are parallel to the chosen ones.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: permutation and combination

Parallel is for lines/rays.

When I see (5,6,7), I think of a point

A vector can be parallel to a plane.

Also, the definition I gave is a bit more precise as a vector cannot lie in a plane.

---

“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
The knowledge of some things as a function of age is a delta function.

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: permutation and combination

Question.
Find the number of 7 letter words that can be formed using the letters of the word SUCCESS so that the two C are together but no two S are together?

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friendship is tan 90°.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: permutation and combination

hi

Treat the CCs as if that was a single letter and work out the answer.  Then also treat the SS and SSS as a single letter (lots of ways)  and subtract.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: permutation and combination

But the ways in which SS and SSS will come together will also include the cases when CC are not together.

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friendship is tan 90°.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: permutation and combination

Hi;

Use the method of slashes, you will get 24.

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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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: permutation and combination

hi bobbym,

I don't know what that is.  I've just had a re-think like this:

With the CC together restriction there are 6 'letters' : U E (CC) S S S

If the S must be separate the 'words' must have the format:

<non s> <s> <non s> <s> <non s> <s> 

Or

<s> <non s> <s> <non s> <s> <non s>

For each of these formats there are 3! ways of filling the <non s> spaces and no choice about the <s> spaces.

So why isn't the answer 3! + 3! = 12 ?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: permutation and combination

What about

<s><non s><non s><s><non s><s>

<s><non s><s><non s><non s><s>

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Bassaricyon neblina

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: permutation and combination

hi Olinguito

Thank you so much.  Now I see it all.  And that will make 24.  I've found it is usually a good thing to agree with bobbym. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: permutation and combination

Hi;

I've found it is usually a good thing to agree with bobbym.

I have done pretty well disagreeing with that fellow and I ain't about to stop now.

---

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.

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: permutation and combination

oh yes.

I've found it is usually a good thing to agree with bobbym.

no doubt about it.

---

friendship is tan 90°.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: permutation and combination

Problem: In how many ways can I permute 5 couples in a row of 10 chairs such that nobody sits with their own partner?

---

'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: permutation and combination

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.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: permutation and combination

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: permutation and combination

There is a formula and possibly a generating function. I will post the explanation when I get back. See you later.

Here is the formula:

where n is the number of couples.

---

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.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: permutation and combination

Appears from the blue?!

---

'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: permutation and combination

You know that I am more concerned with computing the answer than long winded explanations. There are explanations for this and I can send you to them.

Anyway, does it work satisfactorily?

---

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.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: permutation and combination

Yes, please send them

---

'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.