Question

Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point.

[Hint: Number of straight lines =¹⁸C₂ – ⁵C₂ + 1]

Answer 1

We know that,

ⁿC_r

According to the question,

Number of points = 18

Number of Collinear points = 5

Number of lines form by 18 points = ¹⁸C₂

For 5 points to be collinear = ⁵C₂

The number of lines that can be formed joining the point, = ¹⁸C₂–⁵C₂ + 1

= 153-10+1

= 144