Lecture 08 Counting Profs. Koike and Yukita Discrete Systems I Lecture 08 Counting Profs. Koike and Yukita

1. Basic counting principles

Examples

2. Factorial

3. Binomial coefficients

4. Permutations

Example

Example(continued)

Permutations with Repetitions

Example

Example(continued)

Example

5. Combinations

Binomial Theorem

6. The Pigeonhole Principle

Generalized Pigeonhole Principle

7. The Inclusion-Exclusion Principle

8. Ordered Partitions

Ordered partitions 1

Example

Unordered partition

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9