A set of 3 points is chosen randomly from the grid.

Question

Assuming that each set has equal probability of being chosen, what is the probability that the three points lie in a straight line?

The grid looks something like this:

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Answer 1

9 Choose 3 = 9C3 = 9! / (3!*(9-3)!) = 84

There are 84 groups of 3 numbers to consider whether these three points form a straight line

Solutions groups are: three horizontal rows, three vertical rows, and two diagonals. That's 8 groups.

If each point has an equal probability of appearing in the 3 points chosen, then:

P(straight line) = number of solutions / total possibilities = 8 / 84 = 2 / 21