Consider a regular 8x8 chessboard. Precisely 6 distinct squares are chosen randomly on the chessboard.
Determine the probability that they lie in the same diagonal.
There are 4 diagonals of length 6, 4 of length 7 and 2 of length 8.
The 4 of length 6 each accaount for 1 possibility.
The 4 of length 7 each account for C(7,6) = 7 possibilities.
The 2 of length 8 each account for C(8,6) = 28 possibilities.
Total possibilities: 4 + 4*7 + 2*28 = 88.
The denominator is C(64,6) = 74974368.
Probability is 88/74974368 = 11/9371796 =~ 0.0000011737344688, or 1 in 851981.454545455.
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Posted by Charlie
on 2024-07-18 15:41:57 |
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