Probabilities in a drawer
Source: Indonesian MO (INAMO) 2009, Day 2, Problem 5
August 8, 2009
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Problem Statement
In a drawer, there are at most balls, some of them are white, the rest are blue, which are randomly distributed. If two balls were taken at the same time, then the probability that the balls are both blue or both white is . Determine the maximum amount of white balls in the drawer, such that the probability statement is true?