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**13-2 Permutations with Repetitions and Circular Permutations**

Pre Calc A

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**Permutations with Repetitions**

The number of permutations of n objects of which p are alike and q are alike can be found by

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**How many 9 letter patterns can be formed from the letters of the word**

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

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**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

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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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EXAMPLE 6 Find permutations with repetition Find the number of distinguishable permutations of the letters in a. MIAMI and b. TALLAHASSEE. SOLUTION MIAMI.

EXAMPLE 6 Find permutations with repetition Find the number of distinguishable permutations of the letters in a. MIAMI and b. TALLAHASSEE. SOLUTION MIAMI.

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