TS EAMCET · Maths · Permutation Combination
Number of triangles whose vertices are the points \((x, y)\) in the XY-plane with integer coordinates satisfying \(0 \leq x \leq 4\) and \(0 \leq y \leq 4\) is
- A \(2300\)
- B \(2260\)
- C \(2160\)
- D \(2230\)
Answer & Solution
Correct Answer
(C) \(2160\)
Step-by-step Solution
Detailed explanation
Total points: \( (4-0+1) \times (4-0+1) = 25 \) Total ways to choose 3 points: \( \binom{25}{3} = \frac{25 \times 24 \times 23}{3 \times 2 \times 1} = 2300 \) Collinear points on horizontal lines: \( 5 \times \binom{5}{3} = 5 \times 10 = 50 \) Collinear points on vertical lines:…
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