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Geometrical Figures in Permutations and Combinations

In this chapter, we will be dealing with the formulas related to permutations and combinations involving

geometrical figures.

Number of triangles formed by joining the angular points of a polygon

The number of triangles that can be formed by joining the angular points of a polygon of n sides as

vertices are

n(n1)(n2)/6

Number of quadrilaterals formed by joining the vertices of a polygon

The number of quadrilaterals that can be formed by joining the vertices of a polygon of n sides are

n(n1)(n2)(n3)/24 where n>3

Number of triangles formed by joining n points out of which m points are collinear

Consider there be n points in a plane out of which m points are collinear. The number of triangles that

can be formed by joining these n points as vertices are

nC3mC3

Number of triangles formed by joining n points out of which no three points are collinear

Consider there be n points in a plane out of which no three points are collinear. The number of triangles

that can be formed by joining these n points are

n(n1)(n2)/6

Number of straight lines formed by joining n points out of which m points are collinear

Consider there be n points in a plane out of which m points are collinear. The number of straight linesthat can be formed by joining these n points are

nC!mC!" #

Number of straight lines formed by joining n points out of which no points are collinear

Consider there be n points in a plane out of which no points are collinear. The number of straight linesthat can be formed by joining these n points are

n(n1)/2

Number of rectangles formed by using horizontal lines and vertical lines

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The number of rectangles that can be formed by using m hori$ontal lines and n vertical lines are

mC!%nC!

Number of diagonals formed by joining the vertices of a polygon

The number of diagonals that can be formed by joining the vertices of a polygon of n sides are

n(n3)/2

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