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  "body": "\n## Statement\n\nLet $n$ and $k$ be natural numbers with $k \\le n$.\nThen\n$$\\binom{n}{k} = \\binom{n}{n - k}.$$\n\n## Remarks\n\nFor a set $X$ with $n$ elements, the map $S \\mapsto X \\setminus S$ is a bijection from the $k$-subsets of $X$ to the $(n-k)$-subsets. This is a [[bijective proof|0GV2573FP4]] of the identity.\nThe identity makes each row of [[Pascal's triangle|05DME4TZ3K]] read the same from left to right and from right to left.\n\n## Explanations\n\n### L1 human\n\nTo choose $k$ people for a team is the same as to choose the $n - k$ people who stay out.\nFor example, $\\binom{5}{2} = \\binom{5}{3} = 10$.\n",
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