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A chessboard is an 8 by 8 grid of squares. If you randomly choose 3 squares on the board, what is the probability that they lie on the same line, excluding diagonal lines?

 Feb 17, 2020
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\(\text{Pick a square with probability 1}\\ \text{There are then 14 possible squares co-linear with this first square out of 63 possible squares}\\ \text{Having chosen the first two, there are 6 possible squares that will be co-linear with them out of 62 possible squares}\\ p = \dfrac{14}{63}\dfrac{6}{62} = \dfrac{2}{93}\)

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 Feb 17, 2020

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