What is the total number of different 9-letter arrangements that can be formed using the letters in the word CHICANERY? Answer:

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Count Letters and Frequencies: Determine the total number of letters and the frequency of each letter in the word CHICANERY. The word CHICANERY has 9 letters in total. The letter frequencies are as follows: C appears twice, H appears once, I appears once, A appears once, N appears once, E appears once, R appears once, and Y appears once.Calculate Permutations Formula: Calculate the number of different arrangements using the formula for permutations of a multiset. The formula for permutations of a multiset is given by n! / (n1! * n2! * ... * nk!), where n is the total number of items to arrange, and n1, n2, ..., nk are the frequencies of each distinct item. For CHICANERY, n = 9 (total letters), n1 = 2 (frequency of C), and all other ni = 1 (frequencies of the other letters).Apply Formula to CHICANERY: Apply the formula to the word CHICANERY. Using the formula, we get the number of arrangements as 9! / (2! * 1! * 1! * 1! * 1! * 1! * 1! * 1!).Calculate Factorials: Calculate the factorial of 9 and 2. 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362880 2! = 2 × 1 = 2Divide Factorials to Find Arrangements: Divide 9! by 2! to find the number of different arrangements. The number of different arrangements is 362880 / 2 = 181440.

What is the total number of different $9$ -letter arrangements that can be formed using the letters in the word CHICANERY? $\newline$ Answer:

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