perplexus.info :: Probability : Square Choice Conclusion

Square Choice Conclusion (Posted on 2014-11-04)

Consider a regular 8x8 chessboard. Precisely four distinct squares are chosen randomly on the chessboard.

Determine the probability that they lie in the same diagonal.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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solution (spoiler)

Comment 2 of 2 |

There are four each of length-4, 5, 6, and 7 diagonals, and two length 8.

In each, the number of ways is C(n,4).

So the number of ways is 4*(C(4,4) + C(5,4) + C(6,4) + C(7,4)) + 2*C(8,4) = 4 * (1+5+15+35)+2*70 = 364.

There are C(64,4) ways of getting four random places.

So that's a probability of 364/635376 = 182/317688 ~= .000572889123920324.

Posted by Charlie on 2014-11-04 08:33:07

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