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Permutations with Repetitions and Circular Patterns in Pre-Calculus

Learn how to calculate permutations with repetitions and circular permutations, with examples like forming patterns from words and arranging objects in circles.

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Permutations with Repetitions and Circular Patterns in Pre-Calculus

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  1. 13-2 Permutations with Repetitions and Circular Permutations Pre Calc A

  2. Permutations with Repetitions • The number of permutations of n objects of which p are alike and q are alike can be found by

  3. Ex 17: • How many 9 letter patterns can be formed from the letters of the word ISOSCELES • How many eleven letter patterns can be formed from the letters of the word REPETITION

  4. Circular Permutation with a Fixed/Reference Point • If n objects are arranged in a circle then there are (n-1)! permutations of the n objects around the circle. • If n objects are arranged in a circle with a fixed point, then there are n! permutations

  5. Ex last one: • Mr. Kesler is at a picnic that has a circular revolving condiment server. Six condiments are placed on the table. How many ways can the condiments be arranged? • Eleven people are to be seated at a round table where one person is seated closest to the exit. How many possible arrangements of people relative to the exit are possible?

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