Morg
Morg
Joined: Nov 25, 2021
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November 25th, 2021 at 2:15:33 PM permalink
Sort of an odd (and quite specific) question.

On a roll of 9 dice (d6), which are the probabilities of getting:
- three 3 of a kind (xxxyyyzzz configuration)
- at least 4 of a kind?


Many thanks to whoever could help
Dieter
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Dieter
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November 25th, 2021 at 3:57:53 PM permalink
Welcome to the forum.

To clarify, you're asking about a single roll of each die? (Possibly all at once)
May the cards fall in your favor.
Morg
Morg
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November 25th, 2021 at 4:06:11 PM permalink
Hi Dieter, thanks!

That's correct, a single roll of the 9 dice at once.
Dieter
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Dieter
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Thanks for this post from:
Morg
November 25th, 2021 at 4:46:15 PM permalink
... and you don't care what x y and z are, just that they're different?
May the cards fall in your favor.
Dieter
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Dieter
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November 25th, 2021 at 4:59:14 PM permalink
I'm going to have to recuse myself from math until at least Saturday, I'm afraid.

The effects of turkey overdose and liquid holiday cheer are doing a tapdance on my mind.
May the cards fall in your favor.
Ace2
Ace2
Joined: Oct 2, 2017
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Thanks for this post from:
Morg
November 25th, 2021 at 5:26:15 PM permalink
Quote: Morg

Sort of an odd (and quite specific) question.

On a roll of 9 dice (d6), which are the probabilities of getting:
- three 3 of a kind (xxxyyyzzz configuration)
- at least 4 of a kind?


Many thanks to whoever could help
link to original post

For 3 of a kind in xxxyyyzzz format there should be a 20 * 84 * 20 / 6^9 chance
Itís all about making that GTA
Morg
Morg
Joined: Nov 25, 2021
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November 26th, 2021 at 1:55:34 AM permalink
Quote: Ace2

Quote: Morg

Sort of an odd (and quite specific) question.

On a roll of 9 dice (d6), which are the probabilities of getting:
- three 3 of a kind (xxxyyyzzz configuration)
- at least 4 of a kind?


Many thanks to whoever could help
link to original post

For 3 of a kind in xxxyyyzzz format there should be a 20 * 84 * 20 / 6^9 chance
link to original post



Many thanks Ace2!
Could you guide me through the resolution?
Morg
Morg
Joined: Nov 25, 2021
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November 26th, 2021 at 1:56:22 AM permalink
Quote: Dieter

I'm going to have to recuse myself from math until at least Saturday, I'm afraid.

The effects of turkey overdose and liquid holiday cheer are doing a tapdance on my mind.
link to original post



No worries at all of course, many thanks for looking into this!

I hope you had a wonderful Thanksgiving! :)
Ace2
Ace2
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November 26th, 2021 at 8:18:07 AM permalink
20 ways to chose 3 numbers from 6 times 84 ways to place first triple among 9 places, times 20 ways to place second triple among 6 places. Divide by 6^9 total permutations

Assuming this is correct. But this is the method of counting valid permutations
Itís all about making that GTA
teliot
teliot
Joined: Oct 19, 2009
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November 26th, 2021 at 8:38:51 AM permalink
Quote: Ace2

20 ways to chose 3 numbers from 6 times 84 ways to place first triple among 9 places, times 20 ways to place second triple among 6 places. Divide by 6^9 total permutations

Assuming this is correct. But this is the method of counting valid permutations
link to original post

Verified. This is correct. The answer for xxxyyyzzz is 0.003334.

The answer for xxxxabcde is 0.284003
Last edited by: teliot on Nov 26, 2021
Poetry website: www.totallydisconnected.com

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