First slide

Combinations

Question

The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles that can be constructed using these points as vertices is

Easy

A

205
B

210
C

315
D

216

Solution

$=^{12} c_{3} -^{3} c_{3} -^{4} c_{3} -^{5} c_{3} = 205$
The number of triangles that can be constructed using given points as vertices is 205

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