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

The number of diagonals in an octagon is

Ten points are marked on a circle. The number of distinct convex polygons of three or more sides that can be drawn using some or all of the ten points as vertices is:

In how many ways can $5$ boys and $5$ girls stand in a row so that no two girls may be together?

Let $n > 2$ be an integer. Suppose that there are $n$ Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track. Further,each pair of nearest stations is connected by a blue line,whereas all remaining pairs of stations are connected by a red line. If the number of red lines is $99$ times the number of blue lines,then the value of $n$ is:

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