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}