a) You have twelve marbles, four of which are red and eight of which are blue. Arranging the marbles into a circle, what is the probability that any two red marbles end up adjacent?
b) What is the probability that three red marbles end up adjacent?
c) Generalize! This is completely open-ended. Suggested generalizations include adding more marbles or more colors, changing the ratios, even considering the problem in a higher dimension (perhaps with the marbles on the vertices of a cube?).