The sides AB, BC & CA of a triangle ABC have 3, 4 & 5 interior points respectively on them. If the number of triangles that can be constructed using these interior points as vertices is k, then 
is equal to
Text Solution
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(41)
Sol. Total number of triangle = Two points taken from AB and one point either BC or CA + similarly BC + similarly ∠ A + one point each sides.
= 3 C 2 [ 4 C 1 + 5 C 1 ] + 4 C 2 [ 5 C 1 + 3 C 1 ] + 5 C 2 [ 3 C 1 + 4 C 1 ] + 3 C 14 C 15 C 1 = 205
Total – (collinear points used)
= 12 C 3 – ( 3 C 3 + 4 C 3 + 5 C 3 ) = 220 – 15 = 205
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