1. 9.1
Basic Combinatorics

2. What you’ll learn about
Discrete Versus Continuous
The Importance of Counting
The Multiplication Principle of Counting
Permutations
Combinations
Subsets of an n-Set
… and why
Counting large sets is easy if you know the correct formula.

3. Example Arranging Three Objects in Order
How many three-letter codes can be formed using A, B, C, and D if no letter can be repeated?

4. Example Arranging Three Objects in Order
How many three-letter codes can be formed using A, B, C, and D if no letter can be repeated?
List the possibilities in an orderly manner:
So there are 4 • 6 = 24 possibilities.

5. Example Arranging Three Objects in Order
A tree diagram can be used to obtain the same result.

6. Multiplication Principle of Counting…

7. Example Using the Multiplication Principle
If a license plate has four letters followed by three numerical digits. Find the number of different license plates that could be formed if there is no restriction on the letters or digits that can be used.

8. Example Using the Multiplication Principle
If a license plate has four letters followed by three numerical digits. Find the number of different license plates that could be formed if there is no restriction on the letters or digits that can be used.
You can fill in the first blank 26 ways, the second blank 26 ways, the third blank 26 ways, the fourth blank 26 ways, the fifth blank 10 ways, the sixth blank 10 ways, and the seventh blank 10 ways. By the Multiplication Principle, there are 26×26×26×26×10×10×10 = 456,976,000 possible license plates.

9. Permutations of an n-Set
There are n! permutations of an n-set.

10. Example Distinguishable Permutations
Count the number of different 8-letter “words” that can be formed using the letters in the word COMPUTER.

11. Example Distinguishable Permutations
Count the number of different 8-letter “words” that can be formed using the letters in the word COMPUTER.
Each permutation of the 8 letters forms a different word. There are 8! = 40,320 such permutations.

12. Distinguishable Permutations

13. Permutations Counting Formula

14. Combination Counting Formula

15. Example Counting Combinations
How many 10 person committees can be formed from a group of 20 people?

16. Example Counting Combinations
How many 10 person committees can be formed from a group of 20 people?

17. Formula for Counting Subsets of an n-Set

18. Quick Review

19. Quick Review Solutions