Typesetting LaTeX fraction terms to be larger in an equation

I have the following formula in LaTeX, based on Fisher's Exact Test. (NOTE: requires the use of the amsmath package for \binom.)

\begin{equation}
    P(i,j) = \sum_{x=|N(V_i) \cap V_j|}^{\min\{|V_j|, |N(V_i)|}
    \frac{ \binom{|V_j|}{x} \binom{|V - V_j|}{|N(V_i)| - x}}
    {\binom{|V|}{|N(V_i)|}}
\end{equation}

This renders the fraction portion with very small, difficult to read text:

I would like my text more readable, as in the following example:

_{(source: plosone.org)}

What trickery can I use to get LaTeX to render my equation similarly?

This may be what you're looking for:

\begin{equation}
    P(i,j) = \sum_{x=|N(V_i) \cap V_j|}^{\min\{|V_j|, |N(V_i)|} 
    \frac{\displaystyle \binom{|V_j|}{x} \binom{|V - V_j|}{|N(V_i)| - x}}
    {\displaystyle \binom{|V|}{|N(V_i)|}}   
\end{equation}

Thought it might be good to add a reference:

A Guide to LaTeX2e, Kopka & Daly, 1995
Section 5.5 Fine-Tuning Mathematics
5.5.2 Selecting font size in formulas

In my edition, it's on pp 141-142, but this is out of stock on Amazon. The nearest Internet pointer I can find just now is here