PERMUTATIONS Permutation Method of counting when order matters

PERMUTATIONS

Permutation Method of counting when order matters Example: Coming in first, second, or third Combination locks

Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

Examples How many ways can 7 runners finish a race?

Examples How many ways can 7 runners finish a race?

Examples How many ways can 7 runners finish a race?

Permutation Notation n = Number of “objects” to choose from r = Number of “objects” in the arrangement

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Example How many permutations are there for the letters H , O , M , E , S

Example How many permutations are there for the letters H , O , M , E , S

Example How many permutations are there for the letters H , O , M , E , S

Example How many permutations are there for the letters H , O , M , E , S

Examples 20 students volunteer to be on a 3 -person committee. How many different permutations are there?

Examples 20 students volunteer to be on a 3 -person committee. How many different permutations are there?

Examples 20 students volunteer to be on a 3 -person committee. How many different permutations are there?

Examples 20 students volunteer to be on a 3 -person committee. How many different permutations are there?

ASSIGNMENT 12. 6: 1 – 8, 20 – 22, 24, 27 - 29