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  "body": "\n## Summary\n\nCombinatorics is the part of mathematics that studies finite or countable discrete structures.\nIt asks three main types of question about such structures.\nEnumerative questions ask how many structures of a given type exist.\nExistence questions ask if a structure with given properties exists.\nExtremal questions ask how large or small a structure with given properties can be.\n\nIts basic objects are finite sets, arrangements of elements, subsets, partitions and graphs.\nIts basic tools are counting rules, bijections, recurrences, generating functions and the pigeonhole principle.\n\n## Remarks\n\nThe [[rule of sum|0EE2V3CHFK]] and the [[rule of product|0VPK4X73Q0]] are the first counting rules.\n[[Binomial coefficients|092GEF38YD]] count the subsets of a given size of a finite set.\nGraph theory is a large subfield of combinatorics. Its basic notion is a [[graph|0JD5C82QMB]].\n\n## Explanations\n\n### L1 human\n\nCombinatorics is the mathematics of counting and arranging.\nA typical question is: in how many ways can 5 people sit in a row?\nThe answer is $5 \\cdot 4 \\cdot 3 \\cdot 2 \\cdot 1 = 120$, and combinatorics gives general methods for questions of this type.\n",
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