Difference between revisions of "2004 AMC 10A Problems/Problem 5"

Revision as of 10:27, 4 July 2013

Problem

A set of three points is randomly chosen 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?

$\mathrm{(A) \ } \frac{1}{21} \qquad \mathrm{(B) \ } \frac{1}{14} \qquad \mathrm{(C) \ } \frac{2}{21} \qquad \mathrm{(D) \ } \frac{1}{7} \qquad \mathrm{(E) \ } \frac{2}{7}$

Solution

There are $\binom{9}{3}$ ways to choose three points out of the 9 there. There are 8 combinations of dots such that they lie in a straight line: three vertical, three horizontal, and the diagonals.

$\dfrac{8}{\binom{9}{3}}=\dfrac{8}{84}=\dfrac{2}{21} \Rightarrow (C)$

2004 AMC 10A (Problems • Answer Key • Resources)
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Difference between revisions of "2004 AMC 10A Problems/Problem 5"

Revision as of 10:27, 4 July 2013

Problem

Solution

See also