Join the points

If none of the points were colinear, we would have the number of groups of three can be found out of twenty. That is the combination number $( ^{20}_{ 3} )=\frac{20\times19\times18}{2\times3}=1140$ .

When 7 of them are colinear, this means the triangles formed by using exclusively these 7 points will be degenerate and cannot be counted. So the number we need to subtract is $( ^{7}_{ 3} )=\frac{7\times6\times5}{2\times3}=35$ .

The final result is $1140-35=1105.$