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

There are $n$ distinct points on the circumference of a circle. If the number of pentagons that can be formed using these points as vertices is equal to the number of triangles that can be formed,then what is the value of $n$?

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?

Let $S = \{(a, b) : a, b \in \mathbb{Z}, 0 \leq a, b \leq 18\}$. The number of lines in $\mathbb{R}^2$ passing through $(0,0)$ and exactly one other point in $S$ 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

Out of $30$ points in a plane,$8$ of them are collinear. The number of straight lines that can be formed by joining these points is: