NIMCET 2019 Question Paper with solutions

We can get the triangles in two different ways taking two points from the line having 10 points (in ${}_{}^{10}{\mathit{C}}_2^{}$ ways i.e. 45 ways) and one point from the line consisting of 11 points (in 11 ways).
So, the number of triangle $=45\times 11=495$
Now, taking two points from the line having 11 points (in ${}_{}^{11}{\mathit{C}}_2^{}$, i.e. 55 ways) and one point from the line consisting of 10 points (in 10 ways), the number of triangle here is $55\times 10=550$
Hence, required number of triangle$=495+550$
$=1045$