Final answer:
The number of different strings that can be made by rearranging the letters in 'bananananas', use the permutation formula accounting for repeated letters, resulting in 11! / (6! * 2! * 2!).
Step-by-step explanation:
To determine how many different strings can be made by rearranging the letters in the word bananananas, we must consider the number of occurrences of each letter. In this case, the word contains 6 'a' letters, 2 'b' letters, and 2 'n' letters.
The formula to find the number of permutations of a word with repeated letters is n! / (p! * q! * r!...), where n is the total number of letters, and p, q, r, ... are the numbers of each repeating letter.
For the word bananananas, we have a total of 11 letters, so n is 11. We can then calculate the permutations as:
Permutations = 11! / (6! * 2! * 2!)
Using factorials where 11! means 11 factorial (11 * 10 * 9 * ... * 1), and so on for the repeated letters, we can calculate the number of different strings possible.