combinations, not permutations

John E. Franklin · 2012-02-14 11:38:32

I made up this problem after reading at Keene State College
in hopes that someone could enlighten me.
I don't need a complete answer, but anything
at all would be terrific.
Here is the question I came up with:

Given 3 apples, 7 oreos, 13 carrots, 19 cups of water, and 22 slices of toast.
How many ways can you choose 42 of these things.
You are allowed to choose any or all of the apples or toast, or just 18 slices of toast,
as long as it adds up to 42 things.
This is a combination problem. so after you pick up the 42 things, they can be
mixed up in any order and they are considered the same.
Also 3 + 7 is 10 and 13 is 23 and 19 is 42 and 22 is 64 total things.
So I suppose if you pick 42 things, there will be 22 things leftover and so if
you want to just pick 22 things, I think the answer should be the same for the
number of combinations of pickings.
Any discussion is welcome and I do not really need an answer so don't
go overboard unless you are enjoying yourself.
Thanks a lot though since I am quite curious about this problem.
And don't know if it is easy or not.
--JOHN ERIC--

bobbym · 2012-02-14 12:30:53

Hi John E. Franklin;

John E. Franklin · 2012-02-14 12:54:04

Hi bobbym

bobbym · 2012-02-14 14:55:13

Hi John E. Franklin;

John E. Franklin · 2012-02-15 07:30:48

let me test your equation with a trivial example.
one apple
one pear
two bananas
Just those four things.

becomes (devient)

and the results are true! Thanks bobby!
1 way pick all 4.
3 ways pick 3 of the 4.
4 ways to pick 2 of the 4.
3 ways to pick 1 of the 4, since there are only 3 types of fruit.
1 way to pick nothing.
I am thrilled by this incredible formula!!!!!
I know you're not Jane because Jane talks differently.
You can sense these things.
However, I am glad you liked the compliment

bobbym · 2012-02-15 07:41:43

Hi John;

That is very good. People who are programmers generally can understand generating functions alot faster than math types.

John E. Franklin · 2012-02-26 12:26:49

Yeah, I love this polynomial thing.
How long have you known about it?
I'm interested who taught it to you or if you read about it a long time ago.

anonimnystefy · 2012-02-26 13:19:49

Hi JEF

The guys on the forum introduced me to g.f.'s as well.Before that I didn't know anything about them.

I find them very interesting and could've sworn I created a thread about them, but I cannot seem to find it

bobbym · 2012-02-26 14:08:59

Hi John;

Because I learned them before I learned NCr's and NPr's I find them the natural way to do combinatorics.

Hi anonimnystefy;

You are learning about them you just do not know where and how.

anonimnystefy · 2012-02-27 01:27:58

Hi bobbym

Ain't I learning about them in the big Oh thread?

bobbym · 2012-02-27 02:57:20

Yep! Extracting the coefficient of x^r is the whole idea.

anonimnystefy · 2012-02-27 03:00:33

Hi

You keep saying that I don't know I'm learning it, but I know I do and I say that repeatedly and I don't know if that's denial or what.

bobbym · 2012-02-27 03:02:28

No denial at all. We have had other discussions about them too.

Everything I have said to you on almost every question, every choice of program, every choice of paradigm and even choice of what type of mathematics to do, has been a reflection of my view on them.

Math Is Fun Forum

#1 2012-02-14 11:38:32

combinations, not permutations

#2 2012-02-14 12:30:53

Re: combinations, not permutations

#3 2012-02-14 12:54:04

Re: combinations, not permutations

#4 2012-02-14 14:55:13

Re: combinations, not permutations

#5 2012-02-15 07:30:48

Re: combinations, not permutations

#6 2012-02-15 07:41:43

Re: combinations, not permutations

#7 2012-02-26 12:26:49

Re: combinations, not permutations

#8 2012-02-26 13:19:49

Re: combinations, not permutations

#9 2012-02-26 14:08:59

Re: combinations, not permutations

#10 2012-02-27 01:27:58

Re: combinations, not permutations

#11 2012-02-27 02:57:20

Re: combinations, not permutations

#12 2012-02-27 03:00:33

Re: combinations, not permutations

#13 2012-02-27 03:02:28

Re: combinations, not permutations

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