Question

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

• A. 19
• B. 158
• C. 185
• D. 201

Answer 1

Answer: (C)

185

The number of ways of selecting 3 points out of 12 points is ${}^{12}{C}_3$. The number of ways of selecting 3 points out of 7 points on the same straight line is ${}^7{C}_3$. Hence the number of triangles formed will be ${}^{12}{C}_3{-}^7{C}_3=185$.