# Simple combination/permutation odds question

**URL:** <https://boards.straightdope.com/t/simple-combination-permutation-odds-question/778160>\
**Category:** Factual Questions\
**Created:** [January 25, 2017, 5:13pm UTC](https://boards.straightdope.com/t/simple-combination-permutation-odds-question/778160 "2017-01-25T17:13:58Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![Earl\_Snake-Hips\_Tucker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/earl_snake-hips_tucker/32/3269_2.png) [@Earl\_Snake-Hips\_Tucker](https://boards.straightdope.com/u/Earl_Snake-Hips_Tucker)\
**Post date:** [January 25, 2017, 5:13pm UTC](https://boards.straightdope.com/t/simple-combination-permutation-odds-question/778160/1 "2017-01-25T17:13:58Z")

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No, it’s not homework.

I have a population of 24 items. I’m randomly selecting six of them.  
I put the sampled items back in, and sample six again.

What are the chances that there will be no duplicates between the two samples?

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**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\
**Post date:** [January 25, 2017, 6:18pm UTC](https://boards.straightdope.com/t/simple-combination-permutation-odds-question/778160/2 "2017-01-25T18:18:39Z")

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I think it’s 13.8%. 18/24 \* 17/23 \* 16/22 \* 15/21 \* 14/20 \* 13/19.

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**Author:** ![md2000](https://avatars.discourse-cdn.com/v4/letter/m/73ab20/32.png) [@md2000](https://boards.straightdope.com/u/md2000)\
**Post date:** [January 25, 2017, 7:09pm UTC](https://boards.straightdope.com/t/simple-combination-permutation-odds-question/778160/3 "2017-01-25T19:09:55Z")

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Yes. I have a pool of 24 items, an I want to select 6 that are not any of a given set of six.

So first draw, odds are 18/24 that I will pick a good ball.  
(I need to pick one of 18 out of the pool of 24)  
If good - Next draw, 17/23 I pick a good one.  
If good - Next draw, 16/22 I pick a good one.  
etc.  
So…

> [@](#):
>
> I think it’s 13.8%. 18/24 \* 17/23 \* 16/22 \* 15/21 \* 14/20 \* 13/19.

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<div class="post-metadata">

**Author:** ![Earl\_Snake-Hips\_Tucker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/earl_snake-hips_tucker/32/3269_2.png) [@Earl\_Snake-Hips\_Tucker](https://boards.straightdope.com/u/Earl_Snake-Hips_Tucker)\
**Post date:** [January 25, 2017, 7:16pm UTC](https://boards.straightdope.com/t/simple-combination-permutation-odds-question/778160/4 "2017-01-25T19:16:20Z")

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Thanks!