{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "092GEF38YD"
    },
    {
      "field": "specializes",
      "target": "0JPH2Y4DFV"
    },
    {
      "field": "uses",
      "target": "4CZMWQVC30"
    },
    {
      "field": "uses",
      "target": "4HP429BZQ5"
    },
    {
      "field": "uses",
      "target": "4VE006XQ33"
    },
    {
      "field": "uses",
      "target": "4YK46R1QDR"
    },
    {
      "field": "uses",
      "target": "5J25W265JA"
    },
    {
      "field": "uses",
      "target": "6B05T6XHY0"
    },
    {
      "field": "uses",
      "target": "8DEH72QHEA"
    },
    {
      "field": "uses",
      "target": "CRZH89G0J1"
    },
    {
      "field": "uses",
      "target": "D1GQNNRDDN"
    },
    {
      "field": "uses",
      "target": "EY18HD35RG"
    },
    {
      "field": "uses",
      "target": "FJ92Q6VTJH"
    },
    {
      "field": "uses",
      "target": "G6WNYB0WMY"
    },
    {
      "field": "uses",
      "target": "GJ4J77VV60"
    },
    {
      "field": "uses",
      "target": "NDYA85381W"
    },
    {
      "field": "uses",
      "target": "PW313WB7HE"
    },
    {
      "field": "uses",
      "target": "Q4YAST023H"
    },
    {
      "field": "uses",
      "target": "QC4TP5D6HE"
    },
    {
      "field": "uses",
      "target": "TZ6Y9XXQJW"
    },
    {
      "field": "uses",
      "target": "Y4FQT5WPQJ"
    },
    {
      "field": "about",
      "target": "NDYA85381W"
    }
  ],
  "body": "\n## Summary\n\nThe binomial coefficient $\\binom{n}{k}$ is the number of ways to choose $k$ elements from an $n$-element set. These numbers are the coefficients in the expansion of $(x + y)^n$. The node [[binomial coefficient|092GEF38YD]] gives the precise definition.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "inventory": [
      "TH6F05MCH2"
    ],
    "kind": "concept",
    "msc": [
      "05A10"
    ],
    "name": "Binomial coefficient",
    "same_as": {
      "wikidata": "Q209875",
      "wikipedia": "Binomial coefficient"
    },
    "sources": [
      {
        "locator": "Definition and interpretations",
        "url": "https://en.wikipedia.org/wiki/Binomial_coefficient"
      }
    ],
    "specializes": [
      "0PCV9EDJM2"
    ],
    "tag": "0GBZM0MT0F"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/0GBZM0MT0F/",
  "links": [
    {
      "field": "specializes",
      "target": "0PCV9EDJM2"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/0GBZM0MT0F.md",
  "msc": [
    "05A10"
  ],
  "name": "Binomial coefficient",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0GB/0GBZM0MT0F.md",
  "status": null,
  "tag": "0GBZM0MT0F",
  "uri": "m2://0GBZM0MT0F",
  "url": "https://tamnd.github.io/math2/wiki/binomial-coefficient/",
  "writing": {
    "tag": "0GBZM0MT0F",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      }
    ]
  }
}