\documentclass{article}
\begin{document}
\let\foo={
\let\bar=}
\section{Testing Choose}
\def\beep{beep}
\beep\foo\def\beep{BEEP} hello, \beep. \bar\beep.
1. $  a +  b $
2. $  a \choose b $
3. $ a + {b \choose c} + d$
% Should also work with these
4. $ a + \bgroup b \choose c \egroup + d$
% And even our own tokens \let to {}
5. $ a + \foo b \choose c \bar + d$
%% Interesting behaviour! \begingroup ..\endgroup do NOT create boxes!
6. $ a + \begingroup b \choose c \endgroup + d$
%$ a + { b \choose c \egroup + d$
%$ a + \bgroup b \choose c } + d$
% Aha, TeX doesn't like this (says Ambiguous)
%$ a + \frac{b \choose c}{d \choose e} + f$
%\def\open{\bgroup}\def\close{\bgroup}
% It doesn't like this either; it want's a real }
%$ a + \open b \choose c \close + d$
\end{document}