Statistics 简明教程

Statistics - Permutation

排列是对成套对象中的所有或部分进行的排列，而不管排列的顺序如何。例如，假设我们有三个字母：A、B 和 C。我们可以询问有多少种方式可以从该集合中排列 2 个字母。

A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement. For example, suppose we have a set of three letters: A, B, and C. we might ask how many ways we can arrange 2 letters from that set.

排列的定义和给出如下函数：

Permutation is defined and given by the following function:

Formula

其中——

Where −

  1. ${n}$ = of the set from which elements are permuted.

  2. ${r}$ = size of each permutation.

  3. ${n,r}$ are non negative integers.

Example

Problem Statement:

Problem Statement:

一位计算机科学家正在尝试发现一个金融账户的关键词。如果该关键词仅包含 10 个小写字符（例如，集合中的 10 个字符：a、b、c…​w、x、y、z），并且不能重复任何字符，则有哪些不同独特的字符排列方式？

A computer scientist is trying to discover the keyword for a financial account. If the keyword consists only of 10 lower case characters (e.g., 10 characters from among the set: a, b, c…​ w, x, y, z) and no character can be repeated, how many different unique arrangements of characters exist?

Solution:

Solution:

第 1 步：确定此问题属于排列还是组合。由于改变潜在关键词的顺序（例如，ajk 与 kja）将创建一个新的可能性，因此这是一个排列问题。

Step 1: Determine whether the question pertains to permutations or combinations. Since changing the order of the potential keywords (e.g., ajk vs. kja) would create a new possibility, this is a permutations problem.

第 2 步：确定 n 和 r

Step 2: Determine n and r

n = 26，因为计算机科学家从 26 种可能性（例如，a、b、c…​x、y、z）中进行选择。

n = 26 since the computer scientist is choosing from 26 possibilities (e.g., a, b, c…​ x, y, z).

r = 10，因为计算机科学家正在选择 10 个字符。

r = 10 since the computer scientist is choosing 10 characters.

第 2 步：应用公式

Step 2: Apply the formula