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counting and probability intermediate

Problem

A set of three points is chosen randomly from the grid shown. Each three-point set has the same probability of being chosen. What is the probability that the points lie on the same straight line?

problem
Solution
The number of three-point sets that can be chosen from the nine grid points is Eight of these sets consist of three collinear points: 3 sets of points lie on vertical lines, 3 on horizontal lines, and 2 on diagonals. Hence the probability is .
Final answer
\frac{2}{21}