1. 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

2. 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.

3. 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!

4. 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 =

5. 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!