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  "body": "\n## Statement\n\nLet $A$ and $B$ be finite sets with $|A| = k$ and $|B| = n$.\nThen the number of injective functions from $A$ to $B$ is the [[falling factorial|0N5M924N3P]]\n$$(n)_k = n (n - 1) \\cdots (n - k + 1).$$\n\n## Remarks\n\nIf $k \u003e n$, then $(n)_k = 0$, and there is no injection. This is the [[pigeonhole principle|0HGVCWQGY3]].\nAn injection from $\\{1, \\dots, k\\}$ to $B$ is a $k$-permutation of $B$: an ordered list of $k$ distinct elements of $B$.\nFor $k = n$ the count is $n!$, the [[number of permutations|0CEBCS0E0E]].\n\n## Explanations\n\n### L1 human\n\nList the elements of $A$ and give each one an image in $B$ that is not used yet.\nThe first has $n$ choices, the second $n - 1$, and so on, for $k$ steps.\n",
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