Question

There are $12$ points in a plane, out of which $5$ are collinear.Find the number of lines that can be formed by joining these vertices in pairs.

• A. $21$
• B. $65$
• C. $57$
• D. $210$

Answer 1

The correct option is C $57$

The total number of ways to form a line by 12 points are given by ${}^{12}{C}_2$, but since $5$ points are collinear only $1$ line can be formed using these points.

So, ${}^{12}{C}_2$ $-$ ${}^5{C}_2$ $+1$

$=66-10+1=57$