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$$
\left(
\begin{array}{c}
m+n\\
m
\end{array}
\right)
= \frac{(m+n)!}{m!n!}
= \frac{\overbrace{(m+n)(m+n-1)\cdots(n+1)}^\mbox{$m$ factors}}{\underbrace{m(m-1)\cdots 1}_\mbox{$m$ factors}}
$$
I am getting an error and cannot figure out the cause.
I suggest you use \[ \] instead $$ $$ for display math formulas. Like @WillieWong say, with amsmath package You can get a result, perhaps, more appropriate:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
\binom{m+n}{m}
= \frac{(m+n)!}{m!\,n!}
= \frac{\overbrace{(m+n)(m+n-1)\cdots(n+1)}^{m \text{ factors}}}{\underbrace{m(m-1)\cdots 1}_{m \text{ factors}}}
\]
\end{document}
This will do:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
$$
\left(
\begin{array}{c}
m+n\\
m
\end{array}
\right)
= \frac{(m+n)!}{m!n!}
= \frac{\overbrace{(m+n)(m+n-1)\cdots(n+1)}^{\mbox{$m$ factors}}}{\underbrace{m(m-1)\cdots 1}_{\mbox{$m$ factors}}}
$$
\end{document}
The ^\mbox{$m$ factors} was changed to ^{\mbox{$m$ factors}} in two cases (one for superscript and another for subscript), which should be grouped using curly braces.
amsmath, one might as well use \binom instead of doing it by hand in the left hand side. It may also make sense using \text instead of \mbox.
Jul 18, 2016 at 3:29
\text instead of \mbox.
documentclassetc that make this into a MWE, that would be even better.^\mbox{...}and_\mbox{...}are the problems. Better:^{\mbox{...}}. Even better:^{\text{...}}. (Also please have a look at Why is\[ … \]preferable to$$ … $$?)