Question

There are $n$ points in a plane of which $p$ points are collinear. How many lines can be formed from these points?

• A. ${}^n{C}_2{-}^p{C}_2$
• B. ${}^n{C}_2{-}^p{C}_2+1$
• C. ${}^n{C}_2{-}^p{C}_2-1$
• D. ${}^{n-p}{C}_2$

Answer 1

The correct option is B ${}^n{C}_2{-}^p{C}_2+1$

If there are $n$ points, then a number of lines would have been ${}^n{C}_2$.

But here p points are collinear, lines formed if $p$ points were non-collinear would be ${}^p{C}_2$, but instead of these lines they form only one line.

So total number of lines, ${}^n{C}_2{-}^p{C}_2$+$1$