Editing Binomial coefficient (section)

== History and notation ==
[[Andreas von Ettingshausen]] introduced the notation <math>\tbinom nk</math> in 1826,<ref>{{harvtxt|Higham|1998}}</ref> although the numbers were known centuries earlier (see [[Pascal's triangle]]). In about 1150, the Indian mathematician [[Bhaskaracharya]] gave an exposition of binomial coefficients in his book ''[[Līlāvatī]]''.<ref>[[Lilavati]] Section 6, Chapter 4 (see {{harvtxt|Knuth|1997}}).</ref>

Alternative notations include {{math|''C''(''n'', ''k'')}}, {{math|{{sub|''n''}}''C''{{sub|''k''}}}}, {{math|{{sup|''n''}}''C''<sub>''k''</sub>}}, {{math|''C''{{su|p=''k''|b=''n''|lh=0.8}}}},<ref>{{harvnb|Uspensky|1937|p=18}}</ref> {{math|''C''{{su|p=''n''|b=''k''|lh=0.8}}}}, and {{math|''C''{{sub|''n'',''k''}}}}, in all of which the {{mvar|C}} stands for ''[[combination]]s'' or ''choices''; the {{mvar|C}} notation means the number of ways to choose ''k'' out of ''n'' objects. Many calculators use variants of the {{nowrap|{{mvar|C}} notation}} because they can represent it on a single-line display. In this form the binomial coefficients are easily compared to the numbers of [[permutation#k-permutations of n|{{mvar|k}}-permutations of {{mvar|n}}]], written as {{math|''P''(''n'', ''k'')}}, etc.