Among $10$ points in a plane,no three points are collinear and $4$ points are concyclic. How many distinct circles can be drawn using at least $3$ of these points?

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

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

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle formed by these three vertices is equilateral is equal to

If $x$ is the number of ways in which six women and six men can be arranged to sit in a row such that no two women are together and if $y$ is the number of ways they are seated around a table in the same manner,then $x: y=$ (in $: 1$)

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: