The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is

How many different (mutually non-congruent) trapeziums can be constructed using four distinct side lengths from the set $\{1, 2, 3, 4, 5, 6\}$?

In a plane,there are $37$ straight lines,of which $13$ pass through point $A$ and $11$ pass through point $B$. Moreover,no three lines (apart from the lines passing through $A$ and $B$) pass through the same point,and no two lines are parallel. What is the number of points of intersection of the straight lines?

The sides $AB, BC, CA$ of a triangle $ABC$ have respectively $3, 4$ and $5$ points lying on them. The number of triangles that can be constructed using these points as vertices is

If $a, b, c, d$ are four distinct numbers chosen from the set $\{1, 2, 3, \ldots, 9\}$,then the minimum value of $\frac{a}{b} + \frac{c}{d}$ is

Out of $10$ points in a plane,$6$ are collinear. How many triangles can be formed by joining these points?