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EXAMPLE 6 Find permutations with repetition Find the number of distinguishable permutations of the letters in MIAMI and TALLAHASSEE. SOLUTION MIAMI has 5 letters of which M and I are each repeated 2 times. So, the number of distinguishable permutations is = 30. 2! 2! 5! = 120
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EXAMPLE 6 Find permutations with repetition TALLAHASSEE has 11 letters of which A is repeated 3 times, and L, S, and E are each repeated 2 times. So, the number of distinguishable permutations is 3! 2! 2! ! 11! = 39, 916,800 = 831,600.
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GUIDED PRACTICE for Example 6 Find the number of distinguishable permutations of the letters in the word. MALL SOLUTION MALL has 4 letters of which L repeated 2 times. So, the number of distinguishable permutations is = 12. = 4 3 2! 4!
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GUIDED PRACTICE for Example 6 Find the number of distinguishable permutations of the letters in the word. KAYAK SOLUTION KAYAK has 5 letters of which K and A are repeated 2 times. So, the number of distinguishable permutations is = 30. 2! 2! 5! 120 2 2 =
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GUIDED PRACTICE for Example 6 Find the number of distinguishable permutations of the letters in the word. CINCINNATI SOLUTION CINCINNATI has 10 letters of which C repeats 2 times and I and N repeats 3 times. So, the number of distinguishable permutations is = 50,400. 3,628,800 = 2! 3! 3! 10!
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