组合和排列计算器

给定对象的总数和要选择的对象的数量,计算器将找到有/没有重复的排列/组合的数量。它还将从给定的列表中生成 r 组合(r 排列)列表,并显示步骤。

可选,可以用逗号分隔。

如果计算器没有计算出某些东西,或者您发现了错误,或者您有建议/反馈,请将其写在下面的评论中。

您的输入

找出重复次数为$$$\tilde{P}{\left(11,6 \right)}$$$的排列数。

生成重复{B, A, N, A, N, A} 6排列列表。

解决方案

公式是$$$\tilde{P}{\left(n,r \right)} = n^{r}$$$

我们有$$$n = 11$$$$$$r = 6$$$

因此, $$$\tilde{P}{\left(11,6 \right)} = 11^{6} = 1771561$$$

现在,处理清单。

计算每个元素出现的次数: B出现1次, A出现3次, N出现2次 。

因此,生成的列表中的元素数为$$$N = \frac{6!}{1! 3! 2!} = 60$$$ (有关计算阶乘,请参阅 阶乘计算器)。

回答

$$$\tilde{P}{\left(11,6 \right)} = 1771561$$$

生成的列表中的元素数为$$$60$$$A

生成的列表是{B, A, N, A, N, A}, {B, A, N, A, A, N}, {B, A, N, N, A, A}, {B, A, A, N, N, A}, {B, A, A, N, A, N}, {B, A, A, A, N, N}, {B, N, A, A, N, A}, {B, N, A, A, A, N}, {B, N, A, N, A, A}, {B, N, N, A, A, A}, {A, B, N, A, N, A}, {A, B, N, A, A, N}, {A, B, N, N, A, A}, {A, B, A, N, N, A}, {A, B, A, N, A, N}, {A, B, A, A, N, N}, {A, N, B, A, N, A}, {A, N, B, A, A, N}, {A, N, B, N, A, A}, {A, N, A, B, N, A}, {A, N, A, B, A, N}, {A, N, A, N, B, A}, {A, N, A, N, A, B}, {A, N, A, A, B, N}, {A, N, A, A, N, B}, {A, N, N, B, A, A}, {A, N, N, A, B, A}, {A, N, N, A, A, B}, {A, A, B, N, N, A}, {A, A, B, N, A, N}, {A, A, B, A, N, N}, {A, A, N, B, N, A}, {A, A, N, B, A, N}, {A, A, N, N, B, A}, {A, A, N, N, A, B}, {A, A, N, A, B, N}, {A, A, N, A, N, B}, {A, A, A, B, N, N}, {A, A, A, N, B, N}, {A, A, A, N, N, B}, {N, B, A, A, N, A}, {N, B, A, A, A, N}, {N, B, A, N, A, A}, {N, B, N, A, A, A}, {N, A, B, A, N, A}, {N, A, B, A, A, N}, {N, A, B, N, A, A}, {N, A, A, B, N, A}, {N, A, A, B, A, N}, {N, A, A, N, B, A}, {N, A, A, N, A, B}, {N, A, A, A, B, N}, {N, A, A, A, N, B}, {N, A, N, B, A, A}, {N, A, N, A, B, A}, {N, A, N, A, A, B}, {N, N, B, A, A, A}, {N, N, A, B, A, A}, {N, N, A, A, B, A}, {N, N, A, A, A, B} 。