### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Permutation

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A permutation is an arrangement in a definite order of a number of objects taken some or all at a time.

The number of permutations of ‘’ different objects taken ‘’ at a time, where and the objects do not repeat in which is denoted by

i.e .

Number of permutation of ‘’ distinct things take all at a time .

is also denoted as .

Number of permutation of ‘’ distinct things taken ‘’ at a time when repetition is allowed .

Number of permutations of ‘’ objects where are of one kind, ‘’ of second kind  and ‘’ are of kind s-t i.e .

Number of circular permutation of ‘’ objects taken all at a time

Number of circular permutation of ‘’ objects taken ‘’ at a time

.

If clockwise and anticklockwise arrangements are identical then the number of circular permutation of ‘’ objects taken all at a time .

No. of permutations when particular thing is included .

No. of permutations when particular thing is not included .

.

.

Factorials of negative intergrs are not defined.

.

No. of permutation when ‘’ particular things are together .

No. of permutation when ‘’ particular things are identical .

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