How many chords can be drawn through $21$ points on a circle?

In how many ways can $5$ boys and $3$ girls sit in a row so that no two girls are together?

The number of diagonals in a convex polygon with $n$ sides is .....

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?

The number of diagonals in a polygon is $20$. The number of sides of the polygon is:

Let $P$ be a closed polygon with $10$ sides and $10$ vertices (assume that the sides do not intersect except at the vertices). Let $k$ be the number of interior angles of $P$ that are greater than $180^{\circ}$. The maximum possible value of $k$ is