Question

There are $12$ points in a plane of which $5$ are collinear. These points are joined in pairs. Find the number of straight lines formed.

Answer 1

no. of point in a plane $=12$

no. of point in collinear $=5$

to draw a line two points are required

if no. three points are collinear they

no of lines = ${}^{12}{C}_2$

Since $5$ points are collinear, using these 5

points we can draw only one line

$\therefore$ the no. of different lines ${=}^{12}{C}_2{-}^5{C}_2+1$

(single line using collinear points)

${=}^{12}{C}_2{-}^5{C}_2+1$

$=66-10+1$

$=57$