$A$ polygon has $35$ diagonals,then the number of its sides is

If a polygon of $n$ sides has $275$ diagonals,then $n$ is

How many different (mutually non-congruent) trapeziums can be constructed using four distinct side lengths from the set $\{1, 2, 3, 4, 5, 6\}$?

Three out of $6$ vertices of a regular hexagon are chosen at random. The probability that the triangle formed with these three vertices is an equilateral triangle is

In how many ways can $5$ boys and $5$ girls be arranged in a row such that no two girls are together?

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: