Statistics 简明教程

Statistics - Combination 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.

带放回的组合由以下概率函数定义和给出：

Combination 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. ${^nC_r}$ = Unordered list of items or combinations

Example

Problem Statement −

Problem Statement −

有五种冷冻酸奶：香蕉、巧克力、柠檬、草莓和香草。你可以有三个勺子。有多少种口味可以选？

There are five kinds of frozen yogurt: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. What number of varieties will there be?

Solution −

Solution −

此处 n = 5且r = 3。将值代入公式，

Here n = 5 and r = 3. Substitute the values in formula,

Calculator