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I have read this somewhere before but I cannot find the source any more. I have seen the binomial coefficient written as $_nC_k$ as the standard notation (not just because its easy to type nCk). For example, this website: https://courses.lumenlearning.com/math4libarts/chapter/probability-reading-ii/.

Which is a south African website I belive. Where else is this notation used?

user71207
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    In France, I would say that younger people write $\binom nk$, whereas older people might be more used to the notation $C^k_n$. I had never seen $_n C_k$ before. – Will Sep 13 '21 at 13:57
  • In Indonesia we use all – acat3 Sep 13 '21 at 14:00
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    When I was in highschool in the United States we used $~_nC_k$ but in college it was always $\binom{n}{k}$. I expect that the issue was exacerbated by the fact the nPr and nCr notation was used on the texas instruments graphing calculators which were becoming more prominent in the education process here, and so highschool textbooks which were written with these calculators specifically in mind matched notation. – JMoravitz Sep 13 '21 at 14:04
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    I think the rise of $\binom{n}{k}$ notation is related to TeX's introduction of n \choose k command and later LaTeX's \binom{n}{k}. Before TeX it was difficult (and expensive) to typeset it this way so variants of $C(n,r)$ are more common. – user10354138 Sep 13 '21 at 14:10
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    There was also a time where the Pochhammer Symbol was used instead for the purpose of binomial coefficients by some authors, $(n)_k$... The end result is that if you spend time around binomial coefficients written by multiple authors, you should familiarize yourself with what notations are possible and should look to see what notations the author you are currently reading is using. In the case of the Pochhammer symbol in particular, be very careful as the notation has been repurposed for several things over the years and depending on context can have completely different meanings. – JMoravitz Sep 13 '21 at 14:17
  • I was brought up to use ${}^nC_k$ but the $n$ had to be at the top. It is pronounced "n choose k". – ancient mathematician Sep 13 '21 at 14:43
  • In Russia, we use $C_n^k$. – mihaild Sep 13 '21 at 17:29

2 Answers2

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South Korea also uses ${}_{n}C_{k}$ as a standard symbol for the binomial coefficient.

HTChoi
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In India people use ${}^nC_r$ You can see here also enter image description here

Kabir Munjal
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