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?

[AMC10 2004A 4.gif](https://artofproblemsolving.com/wiki/index.php/File:AMC10_2004A_4.gif)
$\mathrm{(A) \ } \frac{1}{21} \qquad \mathrm{(B) \ } \frac{1}{14} \qquad \mathrm{(C) \ } \frac{2}{21} \qquad \mathrm{(D) \ } \frac{1}{7} \qquad \mathrm{(E) \ } \frac{2}{7}$
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.
$\dfrac{8}{\binom{9}{3}}=\dfrac{8}{84}=\dfrac{2}{21} \Rightarrow\boxed{\mathrm{(C)}\ \frac{2}{21}}$