It seems there was an issue with the problem statement (the OCR result shows repeated 1s), but I'll assume a common combinatorics problem involving distinct permutations of a word with repeated characters (e.g., "MISSISSIPPI") to demonstrate the solution approach.

Problem Example: Distinct Arrangements of "MISSISSIPPI"

Step 1: Count total characters
Total letters = 11.

Step 2: Count repeated characters

• M: 1
• I: 4
• S: 4
• P: 2

Step 3: Apply permutation formula for duplicates
The number of distinct permutations is:
[ \frac{n!}{c_1! \times c_2! \times ... \times c_k!} ]

Substitute values:
[ \frac{11!}{1! \times 4! \times 4! \times 2!} = \frac{39916800}{1 \times 24 \times 24 \times 2} = \frac{39916800}{1152} = 34650 ]

Answer: 34650

If your problem differs, please provide the correct statement, and I’ll adjust the solution!

\boxed{34650}

作者声明:本文包含人工智能生成内容。