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2004 AIME II Question 2

AIME · 2004 AIME II

Question 2

A jar has $10$ red candies and $10$ blue candies. Terry picks two candies at random, then Mary picks two of the remaining candies at random. Given that the probability that they get the same color combination, irrespective of order, is $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers, find $m + n.$