If there are $m$ parallel lines in each of the two sets of parallel lines that form a parallelogram,then the total number of parallelograms formed is:

Suppose $BC$ is a given line segment in the plane and $T$ is a scalene triangle. The number of points $A$ in the plane such that the triangle with vertices $A, B, C$ (in that order) is similar to triangle $T$ is

How many triangles $(T_n)$ can be formed by joining the vertices of a regular polygon with $n$ sides? If $T_{(n+1)} - T_n = 10$,what is the value of $n$?

Let $S = \{(a, b) : a, b \in \mathbb{Z}, 0 \leq a, b \leq 18\}$. The number of lines in $\mathbb{R}^2$ passing through $(0,0)$ and exactly one other point in $S$ is:

There are $5$ points $P_1, P_2, P_3, P_4, P_5$ on the side $AB$,excluding $A$ and $B$,of a triangle $ABC$. Similarly,there are $6$ points $P_6, P_7, \ldots, P_{11}$ on the side $BC$ and $7$ points $P_{12}, P_{13}, \ldots, P_{18}$ on the side $CA$ of the triangle. The number of triangles that can be formed using the points $P_1, P_2, \ldots, P_{18}$ as vertices is:

If a group of six students including two particular students $A$ and $B$ stand in a row, then the probability of getting an arrangement in which $A$ and $B$ are separated by exactly one student in between them is