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Number of ways of selecting three squares on a chessboard so that all the three be on a diagonal line of the board or parallel to it is
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Verified Answer
The correct answer is:
392
Number of ways
$$
\begin{array}{l}
=\left[\left({ }^{3} \mathrm{C}_{3}+{ }^{4} \mathrm{C}_{3}+{ }^{5} \mathrm{C}_{3}+{ }^{6} \mathrm{C}_{3}+{ }^{7} \mathrm{C}_{3}\right) \times 2+{ }^{8} \mathrm{C}_{3}\right] \times 2 \\
=392
\end{array}
$$
$$
\begin{array}{l}
=\left[\left({ }^{3} \mathrm{C}_{3}+{ }^{4} \mathrm{C}_{3}+{ }^{5} \mathrm{C}_{3}+{ }^{6} \mathrm{C}_{3}+{ }^{7} \mathrm{C}_{3}\right) \times 2+{ }^{8} \mathrm{C}_{3}\right] \times 2 \\
=392
\end{array}
$$
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