Given six line segments of lengths $2, 3, 4, 5, 6, 7$ units,the number of triangles that can be formed by these lines is

Out of $n$ points in a plane,$p$ points are collinear. (No three of the remaining points are collinear). The number of lines that can be drawn passing through these points is:

$15$ lines are concurrent at a point $P$. $A$ line $L$ not passing through $P$ intersects all the $15$ lines and forms triangles with them. Then the number of triangles having $L$ as one of its sides is

Let $n \geq 2$ be an integer. Take $n$ distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points blue and the rest red. If the number of red and blue line segments are equal,then the value of $n$ is

What is the number of diagonals in an octagon?

There are $10$ points in a plane,out of which $4$ are collinear. How many straight lines can be formed by joining any two of these points?