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Probability
Level
4
Find the number of ways of selecting 3 squares on a chess board (8X8) so that the three lie on a diagonal line of the board or parallel to it...
The answer is 392.
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1 solution
Consider a diagonal on the chess board. We can select any 3 squares out of 8. Number of ways of doing this is 8C3. Similarly, considering all the lines parallel to the diagonal and adding the possible cases: 8C3 + 7C3 + ... + 3C3. Since there are lines parallel to the diagonal on both sides: 8C3 + 2*(7C3 + ... + 3C3)
Since there are two diagonal multiply the above result by 2.
Thus, total ways = 2 [8C3 + 2 (7C3 + ... + 3C3)] = 392