Statistics 简明教程

Statistics - Permutation with Replacement

由数字或事物的集合可以按多种方式排列或组合的每一种可能方式，称为排列。概率中带放回的组合是从无序列表中多次选择一个对象。

Each of several possible ways in which a set or number of things can be ordered or arranged is called permutation Combination with replacement in probability is selecting an object from an unordered list multiple times.

带重复排列用以下概率函数定义并给出：

Permutation with replacement is defined and given by the following probability function:

Formula

其中——

Where −

  1. ${n}$ = number of items which can be selected.

  2. ${r}$ = number of items which are selected.

  3. ${^nP_r}$ = Ordered list of items or permutions

Example

Problem Statement:

Problem Statement:

电子设备通常需要个人密码才能操作。此特定设备使用 4 位数字代码。计算有多少种可能的代码。

Electronic device usually require a personal code to operate. This particular device uses 4-digits code. Calculate how many codes are possible.

Solution:

Solution:

每个代码由 10 位数字{0,1,2,3,4,5,6,7,8,9}集合的 r=4 带重复排列表示。

Each code is represented by r=4 permutation with replacement of set of 10 digits{0,1,2,3,4,5,6,7,8,9}