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  "body": "\n## Statement\n\nLet $X$ be a set with $m$ elements, and let $n$ be a positive integer with $n \\le m$.\nCall a string over $X$ a permutation if no letter occurs twice in it.\nThen the number of such strings of length $n$ is $P(m,n) = m(m-1)\\cdots(m-n+1)$.\n\n## Remarks\n\nHere $P(m,n)$ is the [[falling factorial|0N5M924N3P]] $(m)_n$, which equals $m!/(m-n)!$.\nA string of length $n$ with distinct letters is the same as an injective function from $\\{1,\\dots,n\\}$ to $X$.\nSo the count is a special case of the [[number of injections|0X0N833FF8]].\n",
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