The number of straight lines that can be formed by joining $8$ points on a circle is:

If the number of diagonals of a regular polygon is $35$,then the number of sides of the polygon 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

If a polygon of $n$ sides has $560$ diagonals,then $n=$

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:

In a regular $15$-sided polygon with all its diagonals drawn,a diagonal is chosen at random. The probability that it is neither a shortest diagonal nor a longest diagonal is