# 2013C13

Before you, Brilli the Ant places 2013 urns labelled 1 through 2013. In urn $$i$$, there are $$i-1$$ white balls and $$2013 - i$$ black balls. If you randomly choose an urn, and then randomly choose 13 balls without replacement, the probability that all balls are the same color is $$\frac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. What is the value of $$a + b$$?

×