A) \[{{\,}^{8}}{{C}_{3}}\]
B) \[{{\,}^{8}}{{C}_{3}}-{{\,}^{5}}{{C}_{3}}\]
C) \[{{\,}^{8}}{{C}_{3}}-{{\,}^{5}}{{C}_{3}}-1\]
D) none of these
Correct Answer: C
Solution :
Key Idea: If there are \[n\]different points, the total number of triangles formed by these point are\[{{\,}^{n}}{{C}_{3}}.\] The total number of points are 8. So number of triangles formed by these points are \[{{\,}^{8}}{{C}_{3}}.\] But we have to subtract those triangle in which the point lie on a line. \[\therefore \] Required number of ways\[={{\,}^{8}}{{C}_{3}}-{{\,}^{5}}{{C}_{3}}{{-}^{3}}{{C}_{3}}\] \[={{\,}^{8}}{{C}_{3}}-{{\,}^{5}}{{C}_{3}}-1\] Note: The triangle will be formed, if not more than two points in a line.
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