1. Permutations and Combinations
Probability

2. Review…
Factorials…
Special case…

3. Examples
Here you go…

4. Permutations An ordered arrangement of objects.
The number of different permutations of n distinct objects in n!

5. Example
The objective of a 9x9 Sudoku number puzzle is to fill the grid so that each row, each column, and each 3x3 grid contain the digits 1 to 9. How many different ways can the first row of a blank 9x9 Sudoku grid be filled?

6. Solution

7. Example
The teams in the National League Central Division are listed below. How many different final standings are possible?
How many teams, n, are in the Central Division.
Evaluate n!
Chicago Cubs
Cincinnati Reds
Huston Astros
Milwaukee Brewers
Pittsburgh Pirates
St. Louis Cardinals

8. Permutations of n Objects taken r at a time…
The number of permutations of n distinct objects taken r at a time

9. You try
To form a three-digit code with no repeating digits, you need to select 3 digits from a group of 10.
n = 10
r = 3

10. Example
Forty three race cars started a race. How many ways can the cars finish first, second, and third?
How many Objects? 43
Taken what at a time? 3

11. Combinations
A selection of r objects from a group of n objects without regard to order is…

12. Example
Want to buy three CDs from a selection of five CDs. How many combinations are there?
n = 5
r = 3

13. Distinguishable Permutations
The number of n objects, where n1 are of one type, n2 are of another type, and so on is

14. Example
A building contractor is planning to develop a subdivision. The subdivision is to consist of 6 one- story house, 4 two-story houses, and 2 split-level houses. In how many distinguishable ways can the houses be arranged?