Question

If $m$ points on one straight line are joined to $n$ points on another straight line. The number of points of intersection of the line segments thus formed is

• A. $\frac{^{m}C_{2} \cdot\,{}^{n}C_{2}}{4}$
• B. $\frac{mn \left(m-1\right)\left(n-1\right)}{4}$
• C. $\frac{^{m}C_{2} \cdot\,{}^{n}C_{2}}{2}$
• D. $^{m}C_{2} +\,{}^{n}C_{2}$

Answer 1

Answer: (B)

Each selection of $4$ points, two on one line and two on the other will give one point of intersection as desired in the question.
$\therefore $ Required number
$= \,{}^{m}C_{2} \cdot\,{}^{n}C_{2}$
$ =\frac{mn \left(m-1\right)\left(n-1\right)}{4}$