Question

Out of $8$ given points, $3$ are collinear. How many different straight lines can be drawn by joining any two points from those $8$ points?

• A. $26$
• B. $28$
• C. $27$
• D. $25$

Answer 1

The correct option is A

$26$

Explanation for correct option

Calculating the number of straight lines that can be drawn by joining any two points:

Given, there are $8$ points, out of which $3$ are collinear.

Collinear points are those which are in the same line.

Number of ways in which any $2$ points can be chosen from the $8$ points $=$ ${}^{8}C_2$

Number of lines that would have been formed by collinear points if they were non-collinear = ${}^{4}C_2$

So, the required number of lines is:

$$\begin{gathered} ={}^{8}C_2-{}^{4}C_2+1 \\ =26 \end{gathered}$$

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

Hence, the correct answer is Option(A).