Final answer:
There are 997920 ways to rearrange the letters in the word ALBUQUERQUE, considering the repetition of certain letters by applying the permutations formula for letters with repetition.
Step-by-step explanation:
The question asks for the number of ways to rearrange the letters in the word ALBUQUERQUE. To solve this, we have to calculate the permutation of these letters considering the repetitions. The formula to calculate permutations of letters with repetitions is n! / (n1! * n2! * ... * nk!), where n is the total number of letters and n1, n2, ..., nk are the numbers of each repeating letter.
In ALBUQUERQUE, we have:
- A = 2 times
- L = 1 time
- B = 1 time
- U = 2 times
- Q = 1 time
- E = 2 times
- R = 1 time
So, the total number of letters, n, is 11. The factorial of n (11!) represents the total number of ways to arrange 11 unique letters. We then divide by the factorial of the number of times each letter is repeated. Consequently, the number of ways to rearrange the letters in ALBUQUERQUE is:
11! / (2! * 1! * 1! * 2! * 1! * 2! * 1!) = 11! / (4) = 11*10*9*8*7*6*5*4*3 / 4 = 997920 ways.