What is the technique for creating all combinations from three pots of balls?

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SUMMARY

The discussion focuses on generating all combinations from three pots of balls, each containing 20 distinct balls. The technique used is known as the Cartesian product, which allows for the systematic combination of elements from multiple sets. The user seeks methods to output these combinations into spreadsheet software like Excel or LibreOffice Calc. The conversation highlights the importance of understanding the distinctiveness of the balls, which influences the counting method applied.

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  • Understanding of Cartesian products in combinatorial mathematics
  • Basic knowledge of Excel functions and LibreOffice Calc
  • Familiarity with programming concepts for generating combinations
  • Awareness of distinct and indistinct elements in combinatorial problems
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  • Research how to implement Cartesian products in Python using libraries like itertools
  • Learn how to use Excel's CONCATENATE function to combine cell values
  • Explore online combination generators and their algorithms
  • Investigate the use of macros in LibreOffice Calc for automating combination generation
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This discussion is beneficial for mathematicians, data analysts, software developers, and anyone interested in combinatorial mathematics or needing to generate combinations for data analysis tasks.

martine
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Hello,

I'm trying to solve a combination problem and am uncertain what kind of combination exercise this is. It's not school work, but something I came across in my free time, and I'm somewhat stuck...

I have three pots, each with 20 balls.
I want to create all combinations possible by always taking one ball out of each pot and always using all three pots which remain in the same order, resulting in
pot1_a pot2_A pot3_1
pot1_a pot2_A pot3_2
pot1_a pot2_A pot3_3
...
pot1_t pot2_T pot3_20
(_a to _t is the 20 balls in pot1, etc)

What kind of combination technique is this
Is there an easy way to output all combinations into Excel or libre office calc, or an online solver that really gives all combinations? If I know the exact name of this calculation and know what represents what in the equation I could search myself, but at the moment I'm at a loss
 
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Is there something distinguishing the balls?
i.e. are each of the balls numbered?

If so, then it's just normal counting.
You can see how it goes if you imagine that the balls in pot 1 are red, pot 2 are white, and the ones in pot 3 are blue.
 

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