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AP EAMCET · Maths · Permutation Combination

Let \(X=\{(a, b) \mid a, b \in Z, 0 \leq a \leq 20,0 \leq b \leq 15\}\). Then the number of rectangles with vertices in set \(X\) is

  1. A \(25100\)
  2. B \(25200\)
  3. C \(25300\)
  4. D \(25000\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(25200\)

Step-by-step Solution

Detailed explanation

Number of distinct x-coordinates: \(20 - 0 + 1 = 21\) Number of distinct y-coordinates: \(15 - 0 + 1 = 16\) Number of rectangles = \(\binom{21}{2} \times \binom{16}{2}\) = \(\frac{21 \times 20}{2} \times \frac{16 \times 15}{2}\) = \(210 \times 120\) = \(25200\)