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==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?

<center>[[Image:AMC10_2004A_4.gif]]</center>

<math> \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} </math>

==Solution==
There are <math>\binom{9}{3}</math> 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.

<math>\dfrac{8}{\binom{9}{3}}=\dfrac{8}{84}=\dfrac{2}{21} \Rightarrow (C)</math>

== See also ==
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=131315 AoPS topic]
{{AMC10 box|year=2004|ab=A|num-b=4|num-a=6}}