# Out of 18 points in a plane,

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]

Solution:

We know that,

nCr

$=\frac{\mathrm{n} !}{\Gamma !(\mathrm{n}-\mathrm{r}) !}$

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, = 18C25C2+1

$=\frac{18 !}{2 ! 6 !}-\frac{5 !}{2 ! 3 !}+1$

=153-10+1

=144