# 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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