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**jacks****Member**- Registered: 2012-11-21
- Posts: 128

6 Dice are thrown simultaneously. Then the probability that exactly 3 of them show the same face and remaining 3 shows different face, is

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,375

Different face from the 3 or different from each other too?

Is this okay 4,4,4 and 5,5, 2 or must it be like this 6,6,6, and 1,3, 5?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**jacks****Member**- Registered: 2012-11-21
- Posts: 128

like this 6,6,6, and 1,3, 5

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,375

Hi;

I am getting 25 / 162 as the answer.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**jacks****Member**- Registered: 2012-11-21
- Posts: 128

Yes bobbym you are Right.

would you like to explain it to me

Thanks

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,375

Hi jacks;

Standard yahtzee problem ( modified for 6 die ). That is the method I used.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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What is the theory of gf's?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,375

Hi Agnishom;

Generating functions are really a shortcut way to do all types of counting problems. They turn combinatorics and probability problems into computational ones.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**jacks****Member**- Registered: 2012-11-21
- Posts: 128

Thanks bobbym.

bobbym would you like to give me an idea about generating function

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,375

Hi jacks;

How many ways can you select 3 balls from a pile or 4 red balls, another pile of 3 yellow balls and a pile of 2 blue balls.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Hi bobbym

You have some unmatched parenthesis in there...

That's LaTeX, not Lisp.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,375

Hi;

Thanks, I have repaired the typo.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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