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

If three vertices are chosen from the six vertices of a regular hexagon and joined to form a triangle,what is the probability that the triangle formed is an equilateral triangle?

Find the number of marked points on the plane,if when connected pairwise by line segments,the total number of line segments formed is $15$.

$p$ points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is

The crew of an $8$-oar boat is to be chosen from $12$ men,of whom $3$ can row on the stroke side only. The number of ways in which the crew can be arranged is

Let $l_1$ and $l_2$ be two lines intersecting at $P$. 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 if none of these points coincides with $P$,then the number of triangles formed by these eight points is: