Permutations Linear and Circular. Essential Question: How do I solve problems using permutations?

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Presentation transcript:

Permutations Linear and Circular

Essential Question: How do I solve problems using permutations?

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

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:

Example 1 and 2 Solve: 8 P 3 = =

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

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

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

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

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

Assignment Pages , #’s 9-50 all