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?

I am assuming we draw without replacement (not explicitly stated). Hence there are 25*24*23 = 13800 possible draws.

On any draw, we win if exactly two of the three colors are represented. This happens on 12534 of those draws, giving the ratio as the probability. (The actual test used was that at least one of the colors was not represented, and that all three were not the same color.)