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Homework Help: Selecting squares from chessboard

  1. Oct 20, 2013 #1


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    Gold Member

    1. The problem statement, all variables and given/known data
    If three one by one squares are selected at random from the chessboard, then the probability that they form the letter 'L' is

    2. Relevant equations

    3. 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!
  2. jcsd
  3. Oct 20, 2013 #2


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    2017 Award

    Staff: Mentor

    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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