Question

In a plane, there are 10 points of which 4 are collinear. How many different quadrilaterals can be made with the points as vertices?

Answer 1

Answer: 185

Step-by-step explanation:

Label all the points as A,B,C,D,E,F,G,H,I,J

Quadrilaterals are combinations of 4 points (ABCD, AEFG ..etc) if no three points are collinear( else it will be triangle ) or if no 4 points are collinear( else it will be a straight line.

Therefore total combinations = ¹⁰C₄

total combinations where three points are collinear = ⁴C₃ X 6 (selecting 3 collinear points and 1 no collinear)

total combinations where 4 points collinear =  1

therefore total ways = 210 - 24 - 1 = 185