perplexus.info :: Probability : Chessboard Squares Lying On The Same Diagonal

Chessboard Squares Lying On The Same Diagonal (Posted on 2024-07-18)

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.

No Solution Yet Submitted by K Sengupta

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Solution

| Comment 1 of 2

The number of successful ways is:

4*comb(6,6) + 4*comb(7,6) + 2*comb(8,6)

4*1 + 4*7 + 2*28 = 88

The total number of ways of picking 6 squares from a chessboard is comb(64,6)

= 74974368

The probability is 88/74974368 = 0.000001173734468825399

Posted by Larry on 2024-07-18 11:39:40

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