Final answer:
To find the number of 9-letter words that can be made using the letters in the word 'aaaddeeee', we can use permutations with repetition. The formula used is n! / (n1! * n2! * ... * nk!), where n is the total number of objects and n1, n2, ..., nk are the counts of the repeated objects. After applying the formula, we find that there are 1260 different 9-letter words that can be made.
Step-by-step explanation:
To find the number of 9-letter words that can be made using the letters in the word 'aaaddeeee', we can use the concept of permutations with repetition.
First, let's count how many times each letter appears:
- a: 4 times
- d: 3 times
- e: 4 times
Since we have repetition of letters, we can use the formula for permutations with repetition, which is:
n! / (n1! * n2! * ... * nk!)
Where 'n' is the total number of objects and 'n1', 'n2', ..., 'nk' are the counts of the repeated objects. In this case, we have:
n = 9 (the total number of letters)
n1 = 4 (the count of 'a')
n2 = 3 (the count of 'd')
n3 = 4 (the count of 'e')
Substituting these values into the formula, we get:
9! / (4! * 3! * 4!) = 1260
Therefore, there are 1260 different 9-letter words that can be made using the letters in the word 'aaaddeeee'.