Final answer:
The number of distinct arrangements of the 11 letters in knicknacks, two of the same letters considered identicalis is A. 39,916,800.
Step-by-step explanation:
The number of distinct arrangements of the 11 letters in the word 'knicknacks' can be found using the concept of permutations.
Since there are 11 letters in total, the number of arrangements is 11!.
However, two of the letters, 'k' and 'n', are repeated twice, and therefore, their arrangements need to be considered identical.
To find the correct number of distinct arrangements, we divide the total number of arrangements by the number of ways the repeated letters can be arranged.
The repeated letters 'k' can be arranged in 2! ways, and the repeated letters 'n' can also be arranged in 2! ways.
Therefore, the number of distinct arrangements is given by:
Number of distinct arrangements = 11! / (2! * 2!)
Simplifying this expression gives us the answer:
Number of distinct arrangements = 39,916,800
Therefore the correct answer is A. 39,916,800.