Question

If 7 points out of 12 are in the same straight line, then the number of triangles formed is

• A. 19
• B. 185
• C. 201
• D. None of these

Answer 1

Answer: (B)

185

Answer 2

Numbers of ∆^s = $12C_{3} -^{7}C_{3}\mspace{6mu} = \mspace{6mu}\frac{12.11.10}{1.2.3}\mspace{6mu} - \mspace{6mu}\frac{7.6.5}{1.2.3}$

= 220 – 35 = 185