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An introduction to Permutations and Combinations

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An introduction to the fundamental principles of counting – The Multiplication Principle and The Addition Principle

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An introduction to the fundamental principles of counting – The Multiplication Principle and The Addition Principle

4


An introduction to the fundamental principles of counting – The Multiplication Principle and The Addition Principle

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An introduction to the fundamental principles of counting – The Multiplication Principle and The Addition Principle

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A few examples to illustrate the multiplication and the addition principles of counting.

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Establishment of notations and formulas for factorials and permutations – n! and nPr

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A few examples related to permutations, particularly those involving nPr.

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Permutations of distinct objects in a circle, or circular permutations.

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A few examples related to circular permutations of distinct objects

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Number of selections or combinations of r objects out of n distinct objects. Derivation of nCr or C(n, r)

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An alternate method to derive the formula nCr for combinations.

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Proof of the result C(n,r) = C(n,nr) using formula as well as combinatorial argument.

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A few examples to illustrate the use of nCr in combinatorial problems

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A few more examples to illustrate the use of nCr in combinatorial problems

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Permutations of objects in a row, of which some are identical.

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Permutations of objects in a row, of which some are identical.

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A few examples illustrating permutations of identical objects

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A brief overview of combinations or selections involving Identical objects.

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Selection of any number of objects from a collection of n distinct objects

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Selection of any number of objects from a collection of n distinct objects

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Selection of any number of objects from a collection of n identical objects

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Examples relating to all possible combinations

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Derivation of the formula for calculating the number of divisors of a number.

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Examples illustrating calculation of the number of divisors of a number.

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Division of different objects into groups of fixed sizes
