There are $11$ points in a plane,of which $5$ points are collinear. The total number of distinct quadrilaterals that can be formed with vertices at these points 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

In how many ways can $21$ white balls and $19$ black balls be arranged in a row such that no two black balls are together?

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

In a tournament with five teams,each team plays against every other team exactly once. Each game is won by one of the playing teams and the winning team scores one point,while the losing team scores zero. Which of the following is $NOT$ necessarily true?

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?