Tis the season to be color-coded

How many ordered pairs of positive integers \( (r, s) \), subject to \( 1000 \leq r, s \leq 2000 \), are there such that if \(r\) red Christmas balls and \(s\) silver Christmas balls are randomly placed in a row, then the probability that the 2 Christmas balls, which are located at opposing ends of the row (i.e. the first and the last ball), have the same color is exactly \( \frac {1}{2} \)?

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