Question

Find the number of triangles obtained by joining $10$ points on a plane if :
a) no three of which are collinear
b) four points are collinear

Answer 1

Given that there are $10$ points

a) No. of triangles formed using n points is ${}^n{C}_3$

$\therefore {}^{10}{C}_3$ triangles are formed

b) If $4$ points are collinear then ${}^{10}{C}_3-{}^4{C}_3$.