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 $x$ 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 $: 1$)

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is

How many parallelograms can be formed by a set of $4$ parallel lines intersecting another set of $3$ parallel lines?

How many triangles can be drawn by means of $9$ non-collinear points?

Ten points lie in a plane such that no three of them are collinear. The number of lines passing through exactly two of these points and dividing the plane into two regions,each containing four of the remaining points,is