How many ways can your arrange the letters in the word Cincinnati?

Answer 1

The word "Cincinnati" consists of 9 letters, where the letter "i" appears 2 times and "n" appears 2 times. To find the number of unique arrangements, we use the formula for permutations of multiset: ( \frac{n!}{n_1! \cdot n_2!} ), where ( n ) is the total number of letters and ( n_1, n_2 ) are the frequencies of the repeated letters. Thus, the number of arrangements is ( \frac{9!}{2! \cdot 2!} = \frac{362880}{4} = 90720 ). Therefore, there are 90,720 unique arrangements of the letters in "Cincinnati."