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 2024-10-05,