Selecting squares from chessboard

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SUMMARY

The probability of selecting three one-by-one squares from a chessboard to form the letter 'L' is calculated using combinatorial methods. The total combinations of selecting three squares from 64 is represented as 64C3. The initial calculation identified 49 valid configurations across the chessboard, considering only one orientation of 'L'. However, the discussion highlights that all orientations of 'L' must be considered, indicating that the initial probability calculation is incomplete and requires further analysis to account for all possible orientations.

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  • Understanding of combinatorial mathematics, specifically combinations.
  • Familiarity with chessboard geometry and square arrangement.
  • Knowledge of probability theory and how to calculate probabilities.
  • Basic understanding of geometric shapes and their orientations.
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Homework Statement


If three one by one squares are selected at random from the chessboard, then the probability that they form the letter 'L' is

Homework Equations



The Attempt at a Solution


Total number of ways to choose 3 squares is 64C3. Starting from the 1st square at upperleft corner of 1st row, there is only one way to choose the remaining two squares from the second row adjacent to it such that they form the letter L and this is possible for all the 7 squares(excluding the 8th one) present in 1st row. Thus, it is 7 squares for one row. Similarly, for every 7 rows present(excluding the 8th one), it sums up to 7*7=49. The probability is 49/64C3. But this is not correct!
 
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I think it does not matter how the "L" is oriented. If it appears as "L" from a different side, it counts as well.
 

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