Math Is Fun Forum

CroatBoy

Member

Registered: 2009-10-05

Posts: 9

Combination Problem

Solve the equation for n algebraically.

(n)C(n-2) = 10

Last edited by CroatBoy (2009-10-05 11:12:03)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combination Problem

Hi CroatBoy;

Solve (n (n-1)) / 2 = 10

You get n = 5 and n = - 4

Last edited by bobbym (2009-10-05 11:17:50)

---

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.

simron

Real Member

Registered: 2006-10-07

Posts: 237

Re: Combination Problem

Here's another way:
Think of the formula for

:

Now rewrite

using that. You should be able to solve for n.
Tell me if you need any more help.

Last edited by simron (2009-10-05 11:19:24)

---

Linux FTW

CroatBoy

Member

Registered: 2009-10-05

Posts: 9

Re: Combination Problem

Hi CroatBoy;

Solve (n (n-1)) / 2 = 10

You get n = 5 and n = - 4

But how do you get from (n)(n-1)/2 = 10 to 5 and -4. i know it needs to be factored, but im not sure what the steps are.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combination Problem

Hi;

Expand it:

Times by 2:

And factor:

You can set both equal to 0, like this

Can you solve these 2 linear equations? Do you need help?

Last edited by bobbym (2009-10-05 11:31:27)

---

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.

CroatBoy

Member

Registered: 2009-10-05

Posts: 9

Re: Combination Problem

Here's another way:
Think of the formula for

:

Now rewrite

using that. You should be able to solve for n.
Tell me if you need any more help.

So it would be n!/(n-2)!(n- (n-1) )! = 10 ?

I'm not sure how to solve this.

CroatBoy

Member

Registered: 2009-10-05

Posts: 9

Re: Combination Problem

Hi;

Expand it:

Times by 2:

And factor:

Sorry, that is foreign to me. I haven't solved questions like that in the course.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combination Problem

Hi CroatBoy;

See post #5

---

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.

CroatBoy

Member

Registered: 2009-10-05

Posts: 9

Re: Combination Problem

Hi;

Expand it:

Times by 2:

And factor:

You can set both equal to 0, like this

Can you solve these 2 linear equations? Do you need help?

Thanks alot, makes sense now. Appreciate it!

Last edited by CroatBoy (2009-10-05 11:33:08)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combination Problem

Hi;

Did you understand how to get ( n ( n - 1) ) / 2 = 10 from:

Last edited by bobbym (2009-10-05 11:41:12)

---

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.

CroatBoy

Member

Registered: 2009-10-05

Posts: 9

Re: Combination Problem

Hi;

Did you understand how to get ( n ( n - 1) ) / 2 = 10 from:

I think so, but could you go over it?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combination Problem

Hi;

Simplifcations are possible :

n! / ( n-2 ) ! = n ( n-1 )

n - (n - 2) = 2

So:

Last edited by bobbym (2009-10-05 11:58:48)

---

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.

CroatBoy

Member

Registered: 2009-10-05

Posts: 9

Re: Combination Problem

Hi;

Simplifcations are possible :

n! / ( n-2 ) ! = n ( n-1 )

n - (n - 2) = 2

So:

Why does it become 1?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combination Problem

Hi CroatBoy;

n! / (n -2)! = n * ( n-1) because

n!       = n * (n-1) * (n-2) * (n-3) * ... (1)

(n-2)! = (n-2) * (n-3) * ... (1)  So just cancel:

Last edited by bobbym (2009-10-05 12:11:56)

---

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.

CroatBoy

Member

Registered: 2009-10-05

Posts: 9

Re: Combination Problem

Hi CroatBoy;

n! / (n -2)! = n * ( n-1) because

n!       = n * (n-1) * (n-2) * (n-3) * ... (1)

(n-2)! = (n-2) * (n-3) * ... (1)  So just cancel:

Ok. Thanks.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Combination Problem

Hi CroatBoy;

I might be wrong but you don't sound like I explained it good enough. Tell me where I was vague and I will try to clarify, or someone else will.

---

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.