Question

There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.

Answer 1

Number of point = 10

Number of collinear points = 4

Since 4 out of 10 points are collinear, so the number of linear will be ${(}^4{C}_2-1)$ lie from ${}^{10}{C}_2$

(One is subtracted from ${}^4{C}_2$ to count for the line on which 4 collinear points lie)

$\therefore$ number of linear ${}^{10}{C}_2-{(}^4{C}_2-1)$

${}^{10}{C}_2{-}^4{C}_2+1$

$=\frac{10!}{2!8!}-\frac{4!}{2!2!}+1$

$=\frac{10\times 9}{2}-\frac{4\times 3}{2}+1$

$45-6+1$

$=40$