$\binom{n}{r}$ versus $^n\mathrm{C}_r$ : which notation is more used? I know that the notation $\binom{n}{r}$ is more standard to use since we have a $\LaTeX$ command for it while there is no such thing for $^n\mathrm{C}_r$.
Now, I'm wondering which notation do people use in general when writing by hand. Also, I researched a bit about which countries use which notation mostly but it was futile since I didn't get effective results.
I'd just like to know which notation is more used in general and whether the $^n\mathrm{C}_r$ is used anywhere outside India (I'm Indian, so I'd like to know). Also, I'd like if someone can provide me with some sort of a "poll" of which notation is more used in which countries.
P.s - I have tagged it as a soft question, so I hope this doesn't get closed as "too broad" or by any similar reason. Thanks!
 A: I've seen ${}^n C_r$, but almost vanishingly rarely. The notation $n \choose r$ is easily the most common in my experience, but one sees $C(n, r)$ often too.
A: Update I've added two more notation (seen on this site), which might be relevant. The data change afterwards, mostly in the exact matches in $\LaTeX$Search.
As others stated, I would go with $\binom{n}{r}$(probably never used different notation, although that does not mean much, since I am in math for only few years).
Although for example wiki (search for "binom") gives more options.
As to support my (as well as others) choices I can give you some numbers obtained by searching the terms here ($\LaTeX$Search) and here ($\LaTeX$SpeedSearch). Both hyperlinks link to the page claiming

The Springer LaTeX search lets you search through over 8,223,138 LaTeX code snippets to find the equation you need.

Claim
I did not check all the results, whether they really mean the binomial coefficient, so bear that in mind.
\begin{array}{|c|c|c|c|c|}
\hline
\text{Term} & \text{in }\TeX & \text{Search}^* & \text{SpeedSearch} \\
\hline 
\binom{n}{k} &\verb+\binom{n}{k}+ & 10/1464 & 323 \\
\hline
\binom{n}{r} &\verb+\binom{n}{r}+ & 1/815 & 47 \\
\hline
\binom{n}{2} &\verb+\binom{n}{2}+ & 13/0 & 166 \\
\hline
\binom{n+1}{k} & \verb-\binom{n+1}{k}- & 0/14 & 14 \\
\hline
^nC_r & \verb+^nCr+ & 3/301 & 2 \\
\hline
^nC_k & \verb+^nC_k+ & 13/830 & 3\\
\hline
^nC_2 & \verb+^nC_2+ & 1/619 & 5 \\
\hline
C_r^n & \verb+Cr^n+ & 1/189 & 74 \\
\hline
C_k^n & \verb+C_k^n+ & 1/316 & 13\\
\hline
C_2^n & \verb+C_2^n+ & 6/690 & 8\\
\hline
C_n^r & \verb+C_n^r+ & 3/229 & 7    \\
\hline
C_n^k & \verb+C_n^k+ & 11/287  & 37 \\
\hline
C_n^2 & \verb+C_n^2+ & 39/1471 & 78 \\
\hline
C(n,r) &\verb+C(n,r)+ & 0/1317 & 9\\
\hline
C(n,k) &\verb+C(n,k)+ & 2/1432 & 32 \\
\hline
C(n,2) &\verb+C(n,2)+ & 0/1771 & 4\\
\hline
\end{array}
$^*$ The first number responds to the exact result appearance, the second to the similar one.
Conclusion
Personally I would not really consider the similar results for $\LaTeX$Search. Of course, this statement should be supported by going through the results (and obtaining, that most results are not binomial coefficients). Excluding those (and the $\binom{n+1}{k}$ row) out we get 
\begin{array}{|c|c|c|}
\hline
\text{Type of notation} & \sum Search & \sum SpeedSearch \\
\hline
\text{Notation } \binom{n}{x} & 24 & 536 \\
\hline
\text{Different notation} & 80 & 272\\
\hline
\end{array}
Note I did this mostly for fun. I think these sites have better usage then for some notational statistics.
A: Certainly $n \choose r$, i have never seen ${}^n C_r$. Other than that i see $nCr$ as this is the standard input on a calculator
A: I think the notation $n \choose r$ is most common. I've never seen $^n C_r$, actually, but in cases that it must be written without LaTeX, I often see nCr. Another notation I sometimes see are $ C_r^n$ or $C(n,r)$.
