Question

Combination

7. Ten points lie in a plane, no three of which are collinear. How many lines can be drawn using these points ? How many triangles can be drawn using the vertices chosen from these points? a. b.

Answer 1

Collinear points are points that lie on the same line.

a)

To form a line, all we need to do is select any 2 points , and then join them . The number of ways to select any points (out of 10 distinct points) will be ¹⁰C₂ which is 45.

b)

As all of the points are non-collinear. The number of triangles would have been ¹⁰C₃ which is 120, because to form a triangle, we need to select any three points.

Calculations: