Final answer:
To find how many different 9-letter strings can be made by rearranging distinct characters, the answer is 9 factorial (9!), as each of the 9 positions can be filled by any of the 9 different characters. A is the correct answer.
Step-by-step explanation:
The question relates to the concept of permutations in mathematics. A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement. To determine how many different 9-letter strings can be made by rearranging the characters, we assume that all the characters are distinct. Since each of the 9 positions can be filled by any of the 9 available characters, and because each character can only be used once, the number of different permutations or arrangements is 9!, which means 9 factorial.
9 factorial can be calculated as:
9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
Therefore, the correct answer to how many different 9-letter strings can be made by rearranging the characters is: A) 9!.