Out of $20$ points,no three points are collinear except for $4$ points which are collinear. How many lines can be drawn by joining these points?

Two lines $l_1$ and $l_2$ intersect at a point $P$. If $A_1, B_1, C_1$ are points on $l_1$ and $A_2, B_2, C_2, D_2, E_2$ are points on $l_2$,and none of these points coincide with $P$,how many triangles can be formed using these $8$ points?

Find the total number of rectangles on a normal chessboard.

Let $ABC$ be a triangle. Consider four points $p_1, p_2, p_3, p_4$ on the side $AB$, five points $p_5, p_6, p_7, p_8, p_9$ on the side $BC$, and four points $p_{10}, p_{11}, p_{12}, p_{13}$ on the side $AC$. None of these points is a vertex of the triangle $ABC$. The total number of pentagons that can be formed by taking all the vertices from the points $p_1, p_2, \ldots, p_{13}$ is . . . . . . .

There are $10$ points on the line segment $AB$ excluding $A$ and $B$,and $8$ points on the line segment $AC$ excluding $A$ and $C$. The number of triangles formed using these $18$ points (excluding $A, B,$ and $C$) is:

The number of diagonals of a polygon is $35$. If $A$ and $B$ are two distinct vertices of this polygon,then the number of all those triangles formed by joining three vertices of the polygon having $AB$ as one of its sides is: