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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 162

A bag has marbles of 4 colors: red, white, blue, and green. Assume that if we take four marbles out at random (without replacement), each of the following is equally likely:

(1) one marble of each color is chosen,

(2) one white, one blue, and two reds are chosen,

(3) one blue and three reds are chosen,

(4) all four are red.

What is the smallest possible number of marbles in the bag?

I see you have graph paper.

You must be plotting something

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,658

Hi;

Sorry, I could not meet the time, I was sleeping.

The smallest I can come up with is a bag containing 11 reds, 3 whites, 2 blues and 5 greens.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 162

Its okay, I got 21

I see you have graph paper.

You must be plotting something

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,658

Sorry, that is what I got too, I meant 3 whites not 4!

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**Tpetrie01****Guest**

Sorry, I know this post is old - but can you give me a hint as to how you figured this problem out, bobbym? I've got a similar problem and i want to know which direction i should be thinking in.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,658

Hi;

You would use the multivariate hypergeometric distribution. After that you would try it until you found the right number. This would require some trial and error best done by computer.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**Tpetrie01****Guest**

Thanks! This helps a lot.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,658

You know how to use the multivariate hypergeometric?

**In mathematics, you don't understand things. You just get used to them.**

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**deoxysxxxx****Member**- Registered: Today
- Posts: 4

Is there an easy way to solve it without using some complex formula thing?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,658

Hi;

I do not see how you can avoid either more complicated math or some trial and error. This is a fairly tough problem to me. Where is it being asked?

**In mathematics, you don't understand things. You just get used to them.**

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**deoxysxxxx****Member**- Registered: Today
- Posts: 4

An online class called Art Of Problem Solving. Have you heard of it?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,658

I am a member of the AOPS. I have never seen any solution to this posted over there.

**In mathematics, you don't understand things. You just get used to them.**

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