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  • The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is A. 105 B. 15 C. 175 D. 185

The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is
A. 105
B. 15
C. 175
D. 185

Answers (1)

The answer is the option (d).  

Number of ways of selecting 3 points from given 12 points=^{12}C_3  

 But 3 points from given 7 collinear points does not form triangle.

  Number of ways of selecting 3 points from seven collinear points= ^{7}C_3

 Total number of triangles=^{12}C_3-^{7}C_3=220-35=185

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infoexpert21

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