Question

Out of thirty points in a plane, eight of them are collinear. The number of straight lines that can be formed by joining these points, is

• A. $296$
• B. $540$
• C. $408$
• D. $348$

Answer 1

The correct option is C

$408$

Explanation for correct option

Calculating the number of straight lines formed by joining the points:

Given, there are $30$ points in a plane, out of which $8$ points are collinear.

Number of ways in which $2$ points are chosen out of 30 points to form a line ${=}^{30}{c}_2$

Number of ways in which a line is formed by $2$ points in the $8$ collinear points ${=}^8{c}_2$

The required number of straight lines formed is:

$$\begin{gathered} {=}^{30}{C}_2-{}^8{C}_2+1 \\ =450-43+1 \\ =408 \end{gathered}$$

($+1$ is for the line formed by $8$ collinear points)

Hence, the correct answer is Option(C).