There are $n$ points in a plane,of which $p$ points are collinear. How many lines can be formed from these points?

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?

There are $10$ points on the line segment $AB$ excluding $A$ and $B$,and $8$ points on the line segment $AC$ excluding $A$ and $C$. The number of triangles formed using these $18$ points (excluding $A, B,$ and $C$) is:

Statement-$1$: If a polygon has $45$ diagonals,then the number of sides is $10$. Statement-$2$: Out of $n$ non-collinear points,$2$ points can be selected in $^nC_2$ ways.

Three vertices are chosen randomly from the seven vertices of a regular $7$-sided polygon. The probability that they form the vertices of an isosceles triangle is

Three out of $6$ vertices of a regular hexagon are chosen at random. The probability that the triangle formed with these three vertices is an equilateral triangle is