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

Cartesian Product - dCode

Tag(s) : Combinatorics

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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.

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 | ♣ |

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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Cite as source (bibliography):

*Cartesian Product* on dCode.fr [online website], retrieved on 2024-06-18,

cartesian,product,combination,list

https://www.dcode.fr/cartesian-product

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