Final answer:
The number of different arrangements of 7 letters with repeats is 5040.
Step-by-step explanation:
The number of different arrangements of 7 letters with repeats can be found by using the formula for permutations with repetition. In this case, we have 7 letters and no restrictions on how many times each letter can appear. Therefore, the answer is the total number of permutations of 7 letters, which is 7! (7 factorial).
Using the formula for factorial, we have 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040. So the correct answer is d. 5040.