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.

• A. $140$
• B. $141$
• C. $143$
• D. $144$

Answer 1

Answer: (D)

$144$

The number of straight lines passing through $n$ points out of which $m$ are collinear ${=}_2^n\text{C}{-}_2^m\text{C}+1$

Here, $n=18,m=5$

The number of lines ${=}_2^{18}\text{C}{-}_2^5\text{C}+1$

$=\frac{18\times 17}{1\times 2}-\frac{5\times 4}{1\times 2}+1$

$=153-10+1$

$=144$

Option D is correct