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  "body": "\n## Statement\n\nLet $n$ and $k$ be natural numbers.\nThen\n$$\\binom{n+1}{k+1} = \\binom{n}{k} + \\binom{n}{k+1}.$$\n\n## Remarks\n\nFor $n = 4$ and $k = 1$ it gives $\\binom{5}{2} = \\binom{4}{1} + \\binom{4}{2} = 4 + 6 = 10$.\nCombinatorial proof: fix one element $x$ of an $(n+1)$-element set. A $(k+1)$-subset contains $x$, and then it has $k$ other elements, or it omits $x$.\nThe rule builds [[Pascal's triangle|05DME4TZ3K]] row by row.\n\n## Explanations\n\n### L1 human\n\nEach number in Pascal's triangle is the sum of the two numbers above it.\nThis rule is the same fact: a team of $k+1$ from $n+1$ people either includes a fixed person or does not.\n",
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