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**jacks****Member**- Registered: 2012-11-21
- Posts: 80

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: 86,695

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**jacks****Member**- Registered: 2012-11-21
- Posts: 80

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,695

Hi;

I am getting 25 / 162 as the answer.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**jacks****Member**- Registered: 2012-11-21
- Posts: 80

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: 86,695

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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What is the theory of gf's?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,695

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**jacks****Member**- Registered: 2012-11-21
- Posts: 80

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: 86,695

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

Hi bobbym

You have some unmatched parenthesis in there...

That's LaTeX, not Lisp.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,695

Hi;

Thanks, I have repaired the typo.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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