一道英文排列组合数学题,求高手解答 200分求!

一道英文排列组合数学题,求高手解答 200分求!
这是题目
Determine the number of distinct seven-letter codes (where the letters are chosen from the English alphabet)
such that no letters are repeated in the code and the letters A and B are not next to each other.
This is a difficult problem, so here are some questions to help you solve it.
(a) Is the task described in the problem a uniform task? Explain.
(b) How many distinct codes with no letters repeated in the code are possible?
(c) Consider the second condition of the problem: “the letters A and B are not next to each other.” How can
we express this condition in terms of conditions that we can calculate more easily using the counting principle?
(HINT: Divide this condition into two mutually exclusive conditions.)
(d) Find the number of seven-letter codes that contain AB and have no letters that repeat. To do this, subdivide
this problem into smaller, simpler problems that you can solve. There are two separate calculations involved.
First, you must select the other letters besides AB. (In how many ways can you do that?) Second, you
must place the letters “AB” in the seven-letter code. (In how many ways can you do that?) After you complete
these two calculations, what do you do with those two answers? Explain.
(e) How many seven-letter codes contain BA? Explain.
(f) Based on your answers to (b), (d), and (e), answer the original question.