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October 24th, 2017, 11:58 AM   #1
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Probability of choosing an 'L' shape on a chess board

Someone up for checking my work? This is for fun, not homework.

"Three squares are randomly chosen from an 8x8 chess board. What is the probability that they form an 'L' shape? "

My process: First consider four contiguous squares that form a larger, 2x2 square. Choosing any three squares forms an 'L' shape, so each such square represents four L's. And there are 49 such distinct 2x2 squares on a chess board. So the number of possible L's is 196--four L's per 2x2 square times 49 squares.

All that remains then is to determine the entire overall probability space. That would be n choose k, n=3, and k = 64. Boil that down you get 41664 possible sets of 3 without respect to order. So, we have 196/41664 which is 7/1488.

Did I do good?
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October 24th, 2017, 01:03 PM   #2
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October 24th, 2017, 10:40 PM   #3
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Woo hoo!
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