Friday Puzzle

I adapted this Friday puzzle from one on "Futility Closet" a couple of months back...

A black bag contains 16 billiard balls, some of which are all white and the rest are all black. You randomly pull out two balls at the same time. IF it is EQUALLY likely that the two pulled balls will be the SAME color as DIFFERENT colors, then what is the proportion of the balls within the bag?
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 ANSWER: The bag must contain 6 balls of one color and 10 of the other -- that produces 60 ways of getting a mixed draw, 45 ways of drawing the more common color, and 15 ways of drawing the less common color; i.e. 60 = 45 + 15 the two outcomes are equally likely.