2007 Fermat Problem 25

How many ordered pairs (b,g) of positive integers with 4 \le b \le g \le 2007 are there such that when b black balls and g gold balls are randomly arranged in a row, the probability that the balls on each end have the same colour is \frac{1}{2}?

\textbf{(A)}\ 60\quad \textbf{(B)}\ 62\quad \textbf{(C)}\ 58\quad \textbf{(D)}\ 61\quad \textbf{(E)}\ 59

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