1. If 'n' distinct points are given in the plane such that no three of which are collinear, then the number of line segments formed = nC2 = .

2. If 'n' distinct points are given in the plane such that 'm' of these points are collinear, then the number of line segments formed = (nC2 – mC2) + 1.

3. If 'n' distinct points are given in the plane such that no three of which are collinear, then the number of triangles formed = nC3.

4. If 'n' distinct points are given in the plane such that 'm' of these points are collinear, then the number of triangles formed = (nC3 – mC3).

5. If 'n' distinct points are given on the circumference of a circle, then (i) number of straight lines = nC2, (ii) number of triangles = nC3, (iii) number of quadrilaterals = nC4 and so on.

6. Number of rectangles of any size in a square of size n × n = .

7. Number of squares of any size in a square of size n × n = .

8. Number of rectangles of any size in a rectangle of size m × n (m < n) = (m + 1)(n + 1).

9. Number of squares of any size in a rectangle of size m × n = (m – r + 1)(n – r + 1).

10. If 'm' parallel lines in a plane are intersected by a family of other 'n' parallel lines, then total number of parallelograms so formed is: mC2 × nC2 = .

11. Number of diagonals of a regular polygon with 'n' sides is: .