Question

The number of triangles that can be formed with 10 points as vertices n of them being collinear is 110, then n=
a)3
b)5
c)6
d)4

Answer 1

Well, we can start with the case of n=0 to give us some intuition, since n=0 will be the maximum number of triangles that can be formed. For the special case n=0, the formula for the number of triangles is simply \(\large{10\choose3}=120\). To go from there, think about how many triangles are ruled out when you add collinear points.

Answer 2

b)5

Answer 3

@adarsh\ http://openstudy.com/code-of-conduct Please read this.

Answer 4

Any triangle can be formed by choosing 3 points out of the 10. Now this can be done in three ways:
1) Take three non co-linear points.
2) Take one co-linear points and twq points from the left over 10-n points.
3) Take two co-linear points and one of the non-colinear points.