Q64 / 160 · AP EAMCET 2020 (18 Sep Shift 2) · Mathematics

Find the total number of rectangles on a normal chessboard.

  • A
    \({ }^8 \mathrm{C}_2 \times{ }^8 \mathrm{C}_2\)
  • B
    \({ }^8 \mathrm{C}_2+{ }^8 \mathrm{C}_2\)
  • Correct answer
    C
    \({ }^9 \mathrm{C}_2 \times{ }^9 \mathrm{C}_2\)
  • D
    \({ }^9 P_2 \times{ }^9 P_2\)

Solution

Total number of Rectangles in \(n \times n\) chess board \(=n+1_{c_2} \times n+1_{c_2}\) \(\therefore\) Total Number of Rectangles in \(8 \times 8\) chess Boord \(=9_{c_2} \times 9_{c_2}\) Hence, option (c) is correct.

Hence, the correct answer is option: 'C'.

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