Question:
If there are 19 and 16 points on two distinct parallel lines \(L_{1}\) and \(L_{2}\), respectively, then the total number of triangles that can be formed using these points as vertices, is :
If there are 19 and 16 points on two distinct parallel lines \(L_{1}\) and \(L_{2}\), respectively, then the total number of triangles that can be formed using these points as vertices, is :
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A triangle needs 3 non-collinear points: take all triples and remove those lying wholly on one line.
Updated On: Nov 12, 2026
- \(4983\)
- \(4997\)
- \(5016\)
- \(5049\)
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The Correct Option is C
Solution and Explanation
Total points \(=19+16=35\).
Triples of points: \(\binom{35}{3}=6545\).
Triples on \(L_1\) alone (collinear): \(\binom{19}{3}=969\); on \(L_2\) alone: \(\binom{16}{3}=560\).
Triangles \(=6545-969-560=5016\).
Answer: (3) \(5016\)
Triples of points: \(\binom{35}{3}=6545\).
Triples on \(L_1\) alone (collinear): \(\binom{19}{3}=969\); on \(L_2\) alone: \(\binom{16}{3}=560\).
Triangles \(=6545-969-560=5016\).
Answer: (3) \(5016\)
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