2004 AMC 10A Problem 5

Problem 5 of 25EasierGeometry Counting & Probability

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?

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Solution

The number of three-point sets is

\binom{9}{3} = 84.

The collinear triples are the

3

rows, the

3

columns, and the

2

main diagonals, for a total of

8.

The probability is therefore

\dfrac{8}{84} = \dfrac{2}{21}.

Thus, the correct answer is C.

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