一道英文排列组合数学题,求高手解答200分求!这是题目Determinethenumberofdistinctseven-lettercodes(wherethelettersarechosenfromtheEnglishalphabet)suchthatnolettersarerepeatedinthecodeandthelettersAandB

Question

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.

Answer 1

确定不同的七号代码 （如字母选择由英文字母） 的数量
这样任何字母代码和字母 A 和 B 中重复出现不相邻.
这是一个困难的问题,因此这里有一些帮助您解决的问题.
(a) 有述问题统一的任务的任务吗?介绍.
（可能没有在代码中重复的字母二） 有多少不同代码?
(c) 考虑的问题的第二个条件："A 和 B 的字母是不相邻".如何能
我们表示这种情况的更轻松地使用点票的原则,我们可以计算的条件吗?
(噪声：鸿沟为互相排斥的两个条件的这种情况时）
(d) 查找包含 AB 的七号码的数目并无重复的书信.这样做细分
为更小、 更简单的问题,您可以解决此问题.有两个单独的计算涉及.
第一次,您必须选择 AB.之外的其他字母 （在几种方法可以做,) 第二个,你
必须在 7 号代码的字母"AB".(在几种方法可以做,) 之后您完成
这两个计算,什么你这两个答案?介绍.
(d) 有多少七号代码包含 BA?介绍.
(d) 基于你的回答 (b),(d) 和 (c),回答原来的问题