Statistics 简明教程

Statistics - Circular Permutation

圆排列是 n 个不同的物体可以围绕一个固定圆排列的总方法数。它有两种类型。

Circular permutation is the total number of ways in which n distinct objects can be arranged around a fix circle. It is of two types.

  1. Case 1 − Clockwise and Anticlockwise orders are different.

  2. Case 2 − Clockwise and Anticlockwise orders are same.

circular permutation

Case 1 − Formula

其中——

Where −

  1. ${P_n}$ = represents circular permutation

  2. ${n}$ = Number of objects

Case 2 − Formula

其中——

Where −

  1. ${P_n}$ = represents circular permutation

  2. ${n}$ = Number of objects

Example

Problem Statement

计算以圆桌旁就坐的 4 个人的循环排列，其中考虑 i) 顺时针和逆时针顺序不同以及 ii) 顺时针和逆时针顺序相同。

Calculate circular permulation of 4 persons sitting around a round table considering i) Clockwise and Anticlockwise orders as different and ii) Clockwise and Anticlockwise orders as same.

Solution

在第 1 种情况下，n = 4，使用公式

In Case 1, n = 4, Using formula

应用该公式

Apply the formula

在第 2 种情况下，n = 4，使用公式

In Case 2, n = 4, Using formula

应用该公式

Apply the formula

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