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Calculating Distinguishable Permutations of Various Words

Understand how to find distinguishable permutations of words like MIAMI and TALLAHASSEE. Examples and solutions provided.

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Calculating Distinguishable Permutations of Various Words

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  1. Find the number of distinguishable permutations of the letters in MIAMI and TALLAHASSEE. MIAMI has 5letters of which M and I are each repeated 2times. So, the number of distinguishable permutations is: 5! 120 = = 30 2 2 2! 2! EXAMPLE 6 Find permutations with repetition SOLUTION

  2. TALLAHASSEE has 11letters of which A is repeated 3times, and L, S, and E are each repeated 2times. So, the number of distinguishable permutations is: 39,916,800 11! = 6 2 2 2 3! 2! 2! 2! EXAMPLE 6 Find permutations with repetition = 831,600

  3. MALL ANSWER 12 for Example 6 GUIDED PRACTICE Find the number of distinguishable permutations of the letters in the word.

  4. KAYAK ANSWER 30 for Example 6 GUIDED PRACTICE Find the number of distinguishable permutations of the letters in the word.

  5. ANSWER 50,400 CINCINNATI for Example 6 GUIDED PRACTICE Find the number of distinguishable permutations of the letters in the word.

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