MATH 132 • Discrete Mathematics • Midterm II

Pigeonhole Principle

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Introduction to Counting

Exam like Question 1

Exam like Question 2

Combination & Permutation: Intuition

Exam like Question 3

Exam like Question 4

Combination

Exam like Question 5

Exam like Question 6

Exam like Question 7

Exam like Question 8

Permutation 1

Permutation 2

Exam like Question 9

Exam like Question 10

Exam like Question 11

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

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

Example5

Example 6

Creating Recurrence Relations

Example 7

Example 8

Example 9

Pigeonhole Principle 1

Pigeonhole Principle 2

Pigeonhole Principle 3

Pigeonhole Principle 4

Pigeonhole Principle 5

Counting 1

Counting 2

Counting 3

Counting 4

Counting 5

Counting 6

Binomial Coefficients and Identities 1

Advanced Counting Techniques 1

Advanced Counting Techniques 2

Advanced Counting Techniques 3

Advanced Counting Techniques 4

Advanced Counting Techniques 5

Advanced Counting Techniques 6

Advanced Counting Techniques 7

Recurrence Relations 1

Recurrence Relations 2

Recurrence Relations 3

Recurrence Relation & Advanced Counting Techniques