Explanation:

- The problem involves exchanging books among friends of writer A.

- Writer A has 7 friends.

- Each of these friends has their own set of 4 friends.

- To find the ways books can be exchanged among A's friends, consider the number of permutations.

- The permutation of 7 distinct books (one per friend) among them is 7!.

- Calculate $7!=5040$.

- However, since each friend exchanges 1 book with another, consider just the derangements of 7 items.

- The number of derangements (no item remains in its original position) for 7 items is calculated as:

$$

!n = n! \left( \sum_{i=0}^n \dfrac{(-1)^i}{i!} \right)

$$

- For $n=7$,

$$

!7 = 7! \left(1 - \dfrac{1}{1!} + \dfrac{1}{2!} - \dfrac{1}{3!} + \dfrac{1}{4!} - \dfrac{1}{5!} + \dfrac{1}{6!} - \dfrac{1}{7!}\right) = 1854

$$

- Options are given, but not the correct number from this calculation, indicating oversight or simplification.

- The only possible simplification fitting the multiple-choice is related to exchange mechanics or a limitation.

- Exchanged books circle through combinations, existent permutation states restrict themselves to specific orbits, but real derangement formula shows mechanisms far larger.

- Correct answer choices were either directly adjusted through faulty calculation or corrective step.

- None of these provided is fully accurate against intrinsics, primarily due to heuristic failure; option interpretations must include restrict/exchange constraints based contextual clues.