Notes: 13-2 Repetitions and Circular Permutations

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Presentation transcript:

Notes: 13-2 Repetitions and Circular Permutations How many different arrangements can you make using the letters WOW? three?? OWW WOW WWO This is correct!!

linear arrangement with repetitions: The number of permutations of n objects of which p are alike and q are alike: _n!_ p!q! Example#1: Waikiki has _7! arrangements, 2!3! which is a total of 420 different permutations. divide by the repetitions)

From yesterday: linear arrangement = n! (permutation) Now consider a circular permutation: If n objects are arranged in a circle without a reference point, then there are (n-1)! permutations.

Example#2: If 4 people sit at a square table, how many arrangements are there? (4-1)! 3! = 6 1 2 3 4  These are all considered the same arrangement, just rotated differently.

Example#3: If 4 people sit at a square table, how many arrangements are there if someone wants to sit next to the window? (4)! = 24 1 2 3 4 W i n d o w These are now different arrangements because the window is a reference point and it creates a linear permutation.