MATH 132 • Midterm II • Discrete and Combinatorial Mathematics

Basic Principles of Counting

Counting Examples

Permutations

Permutations Example

Groups and Circular Permutation Example

Identical Objects Example 1

Identical Objects Example 2

Identical Objects Example 3

Combination

n choose r

Committee Example 1

Committee Example 2

Ball Example 1

Ball Example 2

Binomial Theorem

Example 1

Example 2

Example 3

Pascal Identity

Vandermonde's Identity

Example 1

Combinatorial Proof

Example 1

Principle Inclusion-Exclusion

Example 1

Example 2

Distributing Objects into Boxes 1

Distributing Objects into Boxes 2

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Introduction

Homogenous Recurrence Relations

Example 1

Example 2

Example 3

Example 4

Non Homogenous Recurrence Relations

Example 5

Example 6

Creating Recurrence Relations

Example 7

Example 8

Example 9

Counting 1

Counting 2

Counting 3

Counting 4

Counting 5

Counting 6

Binomial Coefficients and Identities 1

Binomial Coefficients and Identities 2

Generalized Permutations and Combinations 1

Generalized Permutations and Combinations 2

Generalized Permutations and Combinations 3

Generalized Permutations and Combinations 4

Generalized Permutations and Combinations 5

Generalized Permutations and Combinations 6

Generalized Permutations and Combinations 7

Generalized Permutations and Combinations 8

Recurrence Relations 1

Recurrence Relations 2

Recurrence Relations 3

Recurrence Relations 4

Recurrence Relations & Generalized Permutations and Combinations

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6