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  "body": "\n## Statement\n\nLet $X$ be a finite set with $|X| = n$.\nThen the number of [[permutations|0BQMWCNS8S]] of $X$ is $n!$.\n\n## Remarks\n\nFor $n = 3$ there are $3! = 6$ permutations of $\\{1, 2, 3\\}$: $123$, $132$, $213$, $231$, $312$ and $321$.\nThe count follows from the [[rule of product|0VPK4X73Q0]]. The image of the first element has $n$ choices, the image of the second has $n - 1$ choices, and so on.\nIt is the case $k = n$ of the [[number of injections|0X0N833FF8]].\n\n## Explanations\n\n### L1 human\n\nTo arrange $n$ different objects in a row, you have $n$ choices for the first place, then $n - 1$ for the second, and so on.\nThe product of these numbers is $n!$.\n",
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