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  "body": "\n## Definition\n\nLet $X$ be a set and let $k$ be a natural number.\nA $k$-combination with repetition of $X$ is a multiset of size $k$ with elements in $X$.\nThat is a function $m : X \\to \\mathbb{N}$ with $\\sum_{x \\in X} m(x) = k$, where $m(x)$ is the multiplicity of $x$.\n\nFor natural numbers $n$ and $k$, the multiset coefficient $\\left(\\!\\binom{n}{k}\\!\\right)$ is the number of $k$-combinations with repetition of an $n$-element set.\n\n## Remarks\n\nThe value is $\\left(\\!\\binom{n}{k}\\!\\right) = \\binom{n + k - 1}{k}$. This is [[stars and bars|009TEMTQKH]].\nFor $X = \\{a, b\\}$ and $k = 2$ there are $3$ multisets: $\\{a, a\\}$, $\\{a, b\\}$ and $\\{b, b\\}$.\nUnlike a [[combination|0JZSRWRBZE]], a combination with repetition can use an element more than once.\n\n## Explanations\n\n### L1 human\n\nA combination with repetition is a choice of $k$ items from $n$ kinds. You can take the same kind more than once, and the order does not matter.\nAn example is a bag of 3 fruits from apples, pears and plums.\n",
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