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

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

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:

The total number of possible ways in which a person can go from $A(0,0)$ to $B(3,3)$ if he can travel only to the right or upward along the grid lines is:

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals

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: