Traingle from a set of points

• Nov 14th 2010, 03:32 AM
kumaran5555
Traingle from a set of points
There are 10 points on a plane out of which 6 are collinear. How many triangles can be formed using these points as vertices.

I have tried it in two methods, and i getting different answers, i am not sure what is wrong in my approach.

first,

10c3 - 6c3 = 100 i.e , taking three points from 10 and subtracting the chances in which all three points have been taken from the collinear points.

second
6c2 * 4c1 + 6c1*4c2 + 4c3 , i.e two from collinear and one from non-collinear + one from collinear and two from non-collinear + all three from non-collinear. I got 120.

I think my first approach has some flaws, can anyone identify them.
• Nov 14th 2010, 04:13 AM
Plato
Both solutions are correct.
BUT they both give 100, not 120.
• Nov 14th 2010, 08:54 PM
kumaran5555
Thanks.

But i am clueless what is wrong in my calculation to get 120 !

20 *4 + 6 * 6 + 4 = 120.

please if you can point out Which part of the second approach is wrong.
• Nov 15th 2010, 02:50 AM
Plato
Quote:

Originally Posted by kumaran5555
Thanks.

But i am clueless what is wrong in my calculation to get 120 !

20 *4 + 6 * 6 + 4 = 120.

please if you can point out Which part of the second approach is wrong.

15 *4 + 6 * 6 + 4 = 100