Permutations and Combinations

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Presentation transcript:

Permutations and Combinations Probability

Review… Factorials… Special case…

Examples Here you go…

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

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?

Solution

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

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

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

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

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

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

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

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?