Combinatorics

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There are three coplanar parallel lines.If any p points are taken on each of the line,the maximum number of triangles with vertices at these points is
a.3p²(p-1) b.3p²(p-1)+1 c.p²(4p-3) d.None of these

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Akshay Ginodia ·2014-05-16 20:50:42

Maximum no. Of triangles will be formed when no 3 points on diff lines are collinear
No. of ways of selecting 3 points =^3pC₃
No. of ways of selecting 3 points on a single line =3* ^pC₃

Subtracting them , we will get our answer as (c)

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Anik Chatterjee but consider the case when the 3 points taken on 3 different lines subtend 180 degrees between them? like when they lie on the common normal to the 3 lines?
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Akshay Ginodia ·2014-05-19 08:09:10

Thats what i said in the first line of my solution..the qstn is asking for maximum number of triangles ..the maximum no. of triangles will be formed when no three points on different lines are collinear..

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Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

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