A) 220
B) 204
C) 205
D) 195
Correct Answer: C
Solution :
[c] We have in all 12 points. Since, 3 points are used to form a triangle, therefore the total number of triangles including the triangles formed by collinear points on AB, BC and CA is \[^{12}{{C}_{3}}=220.\] But this includes the following: The number of triangles formed by 3 points on \[AB=\,{{\,}^{3}}{{C}_{3}}=1\] The number of triangles formed by 4 points on \[BC{{=}^{4}}{{C}_{3}}=4.\] The number of triangles formed by 5 points on \[CA{{=}^{5}}{{C}_{3}}=10.\] Hence, required number of triangles \[=220-(10+4+1)=205.\]You need to login to perform this action.
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