What causes the problem when compiling a displayed equation with \overbrace and \underbrace?

Question

$$
\left(
\begin{array}{c}
m+n\\
m
\end{array}
\right)
= \frac{(m+n)!}{m!n!}
= \frac{\overbrace{(m+n)(m+n-1)\cdots(n+1)}^\mbox{$m$ factors}}{\underbrace{m(m-1)\cdots 1}_\mbox{$m$ factors}}
$$

I am getting an error and cannot figure out the cause.

Answer 1

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}

Answer 2

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.