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Published on October 17th, 2012 In category Education | Maths

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Using combination formula to find numbers of lines, triangles or polygons

Combination formulae for line, triangles & polygonsWe can use the combination formula very easily to find out how many numbers of lines, triangles or polygons can be formed by joining  in the points given on a plane. These kind of questions are very common in the competitive examinations.  Given below are some easy trick to solve these kinds of the problems, you have to just memorise these formulae and you can get top-score in the exams very easily.

If you would like to read and learn the basics and formulae for permutation & combination >> please click here

If there are n given points in a plane and not more than 3 of them are co-linear, then

  • No. of Straight lines that can formed = Combination formula for number of lines
  • No. of Triangles that can be formed = Combination formula for triangle
  • No. of Polygon with r sides can be formed = Combination formula for polygon

This can be generalised as well, if there are ‘m’ co-linear points

  • No. of Straight lines that can formed =Combination formula for straight line m collinear points
  • No. of Triangles that can be formed =Combination formula for triangles m collinear points
  • No. of Polygon with r sides can be formed = Combination formula for Polygon for m collinear points

Some more bonus items 🙂

  •  Number of rectangles of any size in a square of n x n is = number of rectangles using combinations
  • In a rectangle of p x q (p < q) number of rectangles of any size is = number of rectangles
  • In a rectangle of p x q (p < q) number of squares of any size is = number of squares
  • n straight lines are drawn in the plane such that no two lines are parallel and no three lines three lines are concurrent. Then the number of parts into which these lines divide the plane is equal to = Division of the plane