After selecting the colors using the controls, imagine that one color is picked at random from each disk. The order of the combination of colors is not important; for example, red, blue, orange is considered the same combination as red, orange, blue.
The combination chosen sometimes matches your choice of favorable combination.
This Demonstration counts the total number of combinations, the total number of favorable combinations, and by dividing gives the probability that a favorable combination will be chosen.
For example, (as in the first Snapshot) suppose the favorable combination is (Blue, Blue, Yellow) and the disks are colored (Red, Blue), (Red, Blue, Yellow), and (Blue, Yellow). Then there are a total of 12 combinations and two of them are favorable, so the probability of the favorable combination is 2/12 = 1/6.