Question

There are 10 points in a plane, out of which 6 are collinear. If $ N $ is the number of triangles that can be formed, then $ N = $ ?

• A. 120
• B. 850
• C. 100
• D. 150

Hint:

Always subtract the invalid (collinear) combinations when computing triangle count from points.

Answer 1

The Correct Option is C

Total triangles from 10 points: \[ ^{10}C_3 = \frac{10 \cdot 9 \cdot 8}{6} = 120 \] Now subtract the number of triangles formed using only the 6 collinear points, since collinear points don't form valid triangles: \[ ^{6}C_3 = \frac{6 \cdot 5 \cdot 4}{6} = 20 \] So the valid number of triangles: \[ 120 - 20 = \boxed{100} \]