Three numbers are chosen at random from $1$ to $15$. The probability that no two numbers are consecutive is:

There are $n$ points in a plane,of which $p$ points are collinear. How many lines can be formed from these points?

The number of diagonals in a regular polygon of $100$ sides is

Six boys and six girls sit in a row randomly. What is the probability that the six girls sit together?

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

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: