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Cartesian Product

Tool to generate Cartesian products of lists/sets by combining the elements to generate the complete list of possible choices.

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Cartesian Product -

Tag(s) : Combinatorics

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# Cartesian Product

## Cartesian Product Generator

NB: Generation limited to 10000 items

### What is a cartesian product? (Definition)

A Cartesian product is a combination of elements from several sets. The product is written with the symbol ×. It is the totality of the possible combinations among the sets of elements.

### How to generate the list of combinations of a cartesian product?

Enter the sets (1 per line) in the generator table and click on generate.

Example: Generation of all playing card figures (jack, queen, king) of each color (spade, heart, diamond, club)
The first set consists of the 3 figures {J,Q,K}, the second set of the 4 colors {,,,}.
The Cartesian product is:

 J ♠ J ♥ J ♦ J ♣ Q ♠ Q ♥ Q ♦ Q ♣ K ♠ K ♥ K ♦ K ♣

### How to calculate the cardinality of the cartesian product?

The cardinality (total number of combinations) is equal to the multiplication of the cardinality of each set.

Example: A garment with 3 color choices and 5 sizes will have $3 \times 5 = 15$ different possibilities

Example: A padlock with 4 wheels that can define a 4-letter code (26 possible letters for each wheel) will have a cardinality of $26 \times 26 \times 26 \times 26 = 456976$ possible words.

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Cartesian Product on dCode.fr [online website], retrieved on 2024-06-18, https://www.dcode.fr/cartesian-product

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