Question

Ten points are marked on a straight line and 11 points are marked on another straight line. How many triangles can be constructed with vertices from the among the above points?

• A. $495$
• B. $550$
• C. $1045$
• D. $2475$

Answer 1

The correct option is C $1045$

Triangle is formed by picking 3 point 2 from $1^{st}$ line and 1 from $2^{nd}$ of 1 point from $1^{st}$ line or 2 from $2^{nd}$ i.e.
${\Rightarrow }^{10}{C}_2{\times }^{11}{C}_1{+}^{10}{C}_1{+}^{11}{C}_2$
= $\frac{10!}{2!8!}\times \frac{11!}{1!10!}+\frac{10!}{1!9!}\times \frac{11!}{2!9!}$
$\Rightarrow 45\times 11+10\times 55$
$=495+550=1045$