Question

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

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

Answer 1

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

Number of points in a plane$=n$ and number of collinear points$=p$.

We know that as one line has two end points, thus the total number of lines$={{}^{n}C}_2$

Since $p$ points are collinear, then total number of lines drawn$={{}^{p}C}_2$

We also know that as there are $p$ points on the line, therefore the number of lines which contain thee points $=1$

Thus the total number of lines ${=}^n{C}_2{-}^p{C}_2+1$