There are 10 points in a plane, out of these 6 are collinear.

Question

There are 10 points in a plane, out of these 6 are collinear. If $N$ is the number of triangles formed by joining these points, then:

Accepted Answer

We need 3 points to create a triangle. With 10 points number of triangle possible ${}^{10}{C_3}$

Here 6 points are on the same line so we can't make any triangle with those 6 points.

So subtract ${}^{6}{C_3}$.

$$\therefore$$ $N = {}^{10}{C_3} - {}^6{C_3}$

$$ = {{10\,.\,9\,.\,8} \over {1\,.\,2\,.\,3}} - {{6\,.\,5\,.\,4} \over {1\,.\,2\,.\,3}}$$

$= 120 - 20$

$= 100$

Solutions · 1