Statistics 简明教程

Statistics - Combination

组合是对一组对象中所有或部分对象的选择，而不考虑所选对象的顺序。例如，假设我们有一组三个字母：A、B 和 C。我们可能会问从该组中选择 2 个字母的方法有多少种。

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected. For example, suppose we have a set of three letters: A, B, and C. we might ask how many ways we can select 2 letters from that set.

组合被定义并由以下函数给出 −

Combination is defined and given by the following function −

Formula

其中——

Where −

  1. ${n}$ = the number of objects to choose from.

  2. ${r}$ = the number of objects selected.

Example

Problem Statement −

Problem Statement −

一名老师从她的 15 名学生的班级中可以挑选多少个不同的 10 人学生小组？

How many different groups of 10 students can a teacher select from her classroom of 15 students?

Solution −

Solution −

Step 1 - 确定此问题属于排列还是组合。由于改变所选学生的顺序不会创建一个新的组，因此这是一个组合问题。

Step 1 − Determine whether the question pertains to permutations or combinations. Since changing the order of the selected students would not create a new group, this is a combinations problem.

Step 2 - 确定 n 和 r

Step 2 − Determine n and r

n = 15，因为老师从 15 名学生中进行选择。

n = 15 since the teacher is choosing from 15 students.

r = 10，因为老师正在选择 10 名学生。

r = 10 since the teacher is selecting 10 students.

Step 3 - 应用公式

Step 3 − Apply the formula

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