루아텍버전

% binom.tex
% 실행: luatex binom.tex

\def\binom#1#2{
  {#1\choose #2}=
  \directlua{
    local res, n, k = 1, #1, #2
    for j=1,k do
      res = res * (n-k+j)/j
    end
    tex.print(res)
}}

$$\binom{12}{4}$$

\bye