Problem:
Six points on a circle are given. Four of the chords joining pairs of the six points are selected at random. What is the probability that the four chords form a convex quadrilateral?
Answer Choices:
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Solution:
Any four of the six given points determine a unique convex quadrilateral, so there are exactly favorable outcomes when the chords are selected randomly. Since there are chords, there are ways to pick the four chords. So the desired probability is .