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[JEE Advanced 1984] Sides $AB,BC,CA$ of a triangle have $3,4,5$ interior points. The number of triangles formed using these interior points as vertices is ____

VAVidaara Admin Asked 1mo ago 2 views 1 answer
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Sides $AB,BC,CA$ of a triangle have $3,4,5$ interior points. The number of triangles formed using these interior points as vertices is ____

1 Answer

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 1mo ago ▲ 0

Answer: $205$.

$\binom{12}3-\binom33-\binom43-\binom53=220-1-4-10=205$ (subtracting collinear triples on each side).

JEE Advanced 1984 · Permutations and Combinations — verified solution by the Vidaara Team.

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