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October 24th, 2017, 10:58 AM  #1 
Newbie Joined: Oct 2017 From: Hanoi Posts: 4 Thanks: 1  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 196four 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? 
October 24th, 2017, 12:03 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,549 Thanks: 1399 
a+

October 24th, 2017, 09:40 PM  #3 
Newbie Joined: Oct 2017 From: Hanoi Posts: 4 Thanks: 1 
Woo hoo!

September 10th, 2019, 09:43 AM  #4 
Newbie Joined: Sep 2019 From: Slovakia Posts: 3 Thanks: 0  The occasional idea
The most difficult thing was coming to an idea how to avoid double counting of all possible L's on the chessboard.


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