Department of Mathematics
Undergraduate Problem Solving Competition

Problem 3 (11/11 - 11/28) - Marbles

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?).

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