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There are (64 x 63 x 62)/(3 x 2) possible sets of 3 squares;

there are 2 x (32 x 31 x 30)/(3 x 2) sets of 3 the same colour.

Of the 41664 possible threesomes, 9920 are identical in colour, a probability of 0.238

Added: This is identical to the probability of picking three odd or three even numbers from a bag containing the first 64 bingo balls!

Second add-on: I have amended the original answer which was wrong!

The alternative calculation is that after picking one square there are 31 of the remaining 63 which will be of the same colour and if that is so there will be 30 out of 62 to complete the trio. The calculation (simpler!) is thus 31/63 x 30/62 or 930/3906, a probability of 0.238.

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Q: What is the probability if Three squares are randomly chosen from a chess board such that two of them have one color and the third square has another color is?
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