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counting and probability intermediate

Problem

In this square array of 16 dots, four dots are to be chosen at random. What is the probability that the four dots will be collinear? Express your answer as a common fraction.

problem
Solution
If all four of the dots are collinear, it is obvious that it must either be a horizontal line of dots, a vertical line of dots, or a diagonal line of dots. And inspection tells us that there are such collinear sets of 4. And in total, there are . So, the probability is .
Final answer
\frac{1}{182}