Final answer:
To find the number of different anagrams of the word 'uncopyrightable,' we can use the concept of permutations. Taking into account the repeated letters, there are 1,054,920 different anagrams.
Step-by-step explanation:
To find the number of different anagrams of "uncopyrightable," we can use the concept of permutations. Permutations are the different ways to arrange the letters of a word. In this case, we have a word with 16 letters. However, there are repetitions of certain letters (e.g., 't' appears twice, 'e' appears three times), so we need to account for that.
First, we find the total number of arrangements without considering the repeated letters. This is given by 16!. Then, we divide by the factorial of the number of times each repeated letter appears. For example, 't' appears twice, so we divide by 2!. 'e' appears three times, so we divide by 3!. We repeat this process for each repeated letter.
The final formula is:
Number of different anagrams = 16! / (2! × 3!)
Now, we can use a calculator or a math software to evaluate this expression, which gives us the answer: 1,054,920 different anagrams of "uncopyrightable".