A bin contains 25 balls: 10 red, 8 yellow, and 7 blue. We draw three balls at random (without looking!) from the bin, and we will say that we "win" if our three balls represent exactly two colors. (That is, we "win" if we draw two balls of one color and another ball of a different color.)

What is the probability of winning in this particular game?

The number of possible combinations of drawing three balls is
25! / (3! * (25 - 3)!) = 2300. 

The probability of drawing exactly two colors among three drawn balls, i.e., winning this particular game, is 1529/2300 (approximately 66.4782608695652174%).

Posted by Dej Mar on 2008-09-25 12:16:35