1. Permutations Linear and Circular

2. Essential Question: How do I solve problems using permutations?

3. Fast Facts… A permutation is an arrangement of objects in a specific order. When objects are arranged in a row, the permutation is linear. When objects are arranged around a circle, the permutation is circular. “!” (factorial): means multiply by everything less than a number

4. Continued… 4! = 4321 = 24 Calculator: MATH PRB ! To find the number of linear permutations, use the formula P=n! To find the number of linear permutations of “n” objects taken “r” at a time use:

5. Example 1 and 2 Solve: 8 P 3 = =

6. Example 3 Find the number of permutations for the first 5 letters of the alphabet for each situation: – Taken 2 at a time = 20

7. Circular Permutations To find the number of Circular Permutations use the formula: Pc = (n-1)!

8. Example 4 7 different pairs of sunglasses are on a circular display rack. How many ways can the display rack be set up? Pc = (7-1)! Pc = (6)! 720

9. Identical Objects To find the number of permutations with identical objects use the formula:

10. Example 5 Find the number of permutations with identical objects of the letters in each word: ALGEBRABASEBALL 2520 5040

11. Assignment Pages 640-641, #’s 9-50 all