Chapter 11: Advanced Counting

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11.1 Generating permutations and combinations

Lexicographic order

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Generating permutations

GenLexPermutations(n)

PARTICIPATION ACTIVITY

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PARTICIPATION ACTIVITY

CHALLENGE ACTIVITY

Start

Generating r-subsets of a set

PARTICIPATION ACTIVITY

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Additional exercises

EXERCISE

11.2 Binomial coefficients and combinatorial identities

Identities and combinatorial proofs

PARTICIPATION ACTIVITY

2-Subsets

3-Subsets

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The Binomial Theorem

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Pascal’s triangle

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Proof.

PARTICIPATION ACTIVITY

Additional exercises

EXERCISE

11.3 The pigeonhole principle

Proof 11.3.1: The pigeonhole principle.

Proof.

PARTICIPATION ACTIVITY

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Generalized pigeonhole principle

Proof 11.3.2: The generalized pigeonhole principle.

Proof.

PARTICIPATION ACTIVITY

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Proof.

Check Show answer

More uses of the pigeonhole principle

Example 11.3.2: Continued fractions.

PARTICIPATION ACTIVITY

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EXERCISE

11.4 Generating functions

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Using generating functions for counting

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PARTICIPATION ACTIVITY

Reset

Products of generating functions

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PARTICIPATION ACTIVITY

Check Show answer

Binomial Theorem

PARTICIPATION ACTIVITY

Generating functions for counting: Another example

PARTICIPATION ACTIVITY

Additional exercises

EXERCISE

Source