Counting Problem, Why is this difficult

[us3rnotfound]

20 cookies are to be distributed to 10 kids in any way.

In how many ways can the cookies be distributed?

I know it's probably something simple like 10^20, but can someone offer some sort of explanation as to why? I know the number has to be huge, so it's not something simple like 20ncr10.

Thanks

 

[clamum]

I think it's 20^10? I looked at it like binary, say a 32 bit register can hold 2^32 values. Perhaps I've gone full retard though.

 

[Ruptga]

Does every kid have to get at least one cookie?

 

[GodlessAstronomer]

40!/10!10! - 40!/9!11!

Edit - this is wrong, but on the right track. Give me a few minutes.

 

[us3rnotfound]

No, one sample point could be:
1 17
2 0
3 0
4 0
5 3
6 0
7 0
8 0
9 0
10 0

1 is a fatass and 5 is just a dick.

 

[her209]

Do all cookies have to be distributed? In other words, can you have cookies left over?

 

[us3rnotfound]

Do all cookies have to be distributed? In other words, can you have cookies left over?

Assume all the cookies are distributed.

 

[mmntech]

Two each, the fair and easy way.

 

[The Boston Dangler]

since the cookies are unearned income, they are taxed at 40%. i take my 8 cookies and leave.

 

[us3rnotfound]

Pretty much confirmed that it's 10^20:

http://www.fen.bilkent.edu.tr/~otekman/disc/usef.pdf

But some kind of proof would be nice.

The next part of the question: Each kid must get 2 cookies. Now how many ways can the cookies be distributed?

 

[BoberFett]

You give one cookie to any of the 10.

10 possible outcomes

You then give one more cookie to any of 10.

10 x 10 possible outcomes

Repeat this 18 more times.

10^20

 

[her209]

The next part of the question: Each kid must get 2 cookies. Now how many ways can the cookies be distributed?

Wouldn't that just be 1?

 

[Anubis]

 

[us3rnotfound]

Wouldn't that just be 1?

Apparently the cookies are distinguishable.

My gut tells me that it's:

(20 choose 2)x(18 choose 2)x...x(2 choose 2). Is this on the right track? Dr. Pizza hello?

 

[GodlessAstronomer]

No, one sample point could be:
1 17
2 0
3 0
4 0
5 3
6 0
7 0
8 0
9 0
10 0

1 is a fatass and 5 is just a dick.

You should have been more clear up front, I wasted time assuming that the problem would actually be challenging (ie, that every kid needs at least one cookie).

 

[GodlessAstronomer]

Apparently the cookies are distinguishable.

My gut tells me that it's:

(20 choose 2)x(18 choose 2)x...x(2 choose 2). Is this on the right track? Dr. Pizza hello?

FFS man ask the questions properly up front. If you want us to do your homework then just copy the questions verbatim.

 

[BoberFett]

Wouldn't that just be 1?

Unless he's referring to the way in which they are distributed.

Kid1 - Kid2 - Kid3

is different than

Kid3 - Kid2 - Kid1

 

[TuxDave]

If cookies are distinguishable and not every kid needs a cookie, then it's 10^20

Each cookie has to be assigned to a kid. That's 10 different possibilities that the cookie could go to. There's 20 cookies, 10^20.

QED.

Edit Oh.. there's a 2nd part.. one sec

Apparently the cookies are distinguishable.

My gut tells me that it's:

(20 choose 2)x(18 choose 2)x...x(2 choose 2). Is this on the right track? Dr. Pizza hello?

That looks right to me.

 

[xSauronx]

if johncu was here i bet hed know...hes a math nerd, hes not even on aim to ask him though

 

[amdhunter]

3628800

 

[911paramedic]

ffs man ask the questions properly up front. If you want us to do your homework then just copy the questions verbatim.

lmao

 

[DrPizza]

Simple to think about this way. Each cookie is distributed independently.

How many ways are there to distribute just one cookie among 10 kids, assuming you're not going to break the cookie into halves, or quarters, or crumbs, etc., which leads to an incredibly high number of ways, although not infinite as some people might claim. The reason for there not to be an infinite number of possible distributions is that you can only divide a cookie into a finite number of pieces. Even if you divide it into its constituent atoms, that's still a finite number.

Anyway, there are 10 ways to distribute 1 cookie.

How many ways are there to distribute another cookie? 10 ways.

Since they're independent of each other, you can use the counting principle: 10 *10 ways to distribute 2 cookies.

Likewise, 10 * 10 * 10 * . . . * 10 i.e. 10^20
OP is correct, this is the explanation.

 

[DrPizza]

Apparently the cookies are distinguishable.

My gut tells me that it's:

(20 choose 2)x(18 choose 2)x...x(2 choose 2). Is this on the right track? Dr. Pizza hello?

Hello, *now* I read through the thread. Yep, correct again.

edit: and finishing reading through the thread, TuxDave has already confirmed as well. I'm too slow tonight. Back to the gallons of tomato sauce on the stove...

 

[her209]

Simple to think about this way. Each cookie is distributed independently.

How many ways are there to distribute just one cookie among 10 kids, assuming you're not going to break the cookie into halves, or quarters, or crumbs, etc., which leads to an incredibly high number of ways, although not infinite as some people might claim. The reason for there not to be an infinite number of possible distributions is that you can only divide a cookie into a finite number of pieces. Even if you divide it into its constituent atoms, that's still a finite number.

Anyway, there are 10 ways to distribute 1 cookie.

How many ways are there to distribute another cookie? 10 ways.

Since they're independent of each other, you can use the counting principle: 10 *10 ways to distribute 2 cookies.

Likewise, 10 * 10 * 10 * . . . * 10 i.e. 10^20
OP is correct, this is the explanation.

Nice!

 

[aloser]

"One for you, one for me; two for you, one, two for me; three for you, one, two, three for me..."