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  "body": "\n## Statement\n\nLet $A$ and $B$ be finite sets.\nThen the Cartesian product $A \\times B = \\{(a, b) : a \\in A, b \\in B\\}$ is finite and $|A \\times B| = |A| \\cdot |B|$.\n\nMore generally, for finite sets $A_1, \\dots, A_k$, the product $A_1 \\times \\dots \\times A_k$ has $|A_1| \\cdots |A_k|$ elements.\n\n## Remarks\n\nA common form of the rule: a choice is made in $k$ steps, and step $i$ has $n_i$ options, whatever the earlier steps are. Then there are $n_1 n_2 \\cdots n_k$ choices in total.\nThe [[number of functions between finite sets|08QQH9F7G0]] is a direct consequence.\n\n## Explanations\n\n### L1 human\n\nIf you choose one item from a first group and then one item from a second group, you multiply the sizes.\nFor example, with 3 shirts and 4 trousers there are $3 \\cdot 4 = 12$ outfits.\n",
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