Question

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

Answer 1

Answer:

Step-by-step explanation:

We require 3 points to form a triangle. So we have 12 points in total.

So number of triangles possible = No. of ways in which you can select 3 vertices - ( cases giving invalid triangles)

12 C 3 :- All possible ways of selecting 3 points out of 12.

7 C 3 :- Select 3 points out of 7 those were lying on the line. These are the cases that don't form a triangle.

So final ans :- 12 C 3 - 7 C 3 = 185

Answer 2

Hey !

Given :- 7 points out of 12 are in the same straight line.

Solution :- Number of triangles = ¹²C₃ - ⁷C₃

                                                     = 220 - 35

                                       Answer= 185

Good luck !